The web has many online coin auctions, although not as many as there used to be. Some are specific to coins, while others are general purpose auctions that happen to also have coins on them. They each have their own set of rules, which you should be careful to abide by. They each have varying pricing structures for their services as well. Be sure to know what you'll actually pay for a coin including shipping and handling and buyers fees before you participate in an auction.
You should also know something about who you are buying coins from. Most of the general purpose auctions have a ratings system, a thing that would be nice for the coin specific auctions to add (where appropriate). Those who depend on PCGS, NGC and Anacs wouldn't really need this, but those accepting submissions from a large number of third parties would benefit from this kind of feedback service. It's also important to be able to have real names, and contact information such as addresses and phone numbers of sellers online. This is important in case you have to file a fraud case.
This page was originally written in 1998, and is now being updated as of December 2003. Many of the auction pages that were around in 1998 have succumbed to the juggernaut of Ebay. Even some of the larger auctions like yahoo auctions and Amazon's auctions that poured huge amounts of money into their creation are not really top notch competitors for Ebay. They exist, like Apple Macintosh, only for those disgruntled with or kicked out by the big boys. They have much more of the Home Shopping Network type of material than Ebay seems to as well.
The lesson of the past few years is the same as that of Automobiles in the first half of the twentieth century. In 1902 alone at least 50 firms began manufacturing automobiles in the United States. Indiana had more manufacturers than Detroit. By 1939, the big three automobile manufacturers claimed 90% of the market, and most of the rest of the 10% was shared among five other companies. While things sort themselves out faster on the Internet, it is the same process in play here. Basically, if you can live with Ebay, live with Ebay.
There are now several companies making a go out of providing services and support that Ebay doesn't. Paypal started out this way, competing with Ebay's inferior Billpoint services. Now Paypal is a subsidiary of Ebay, they won by providing a service Ebay couldn't, or wouldn't provide. SquareTrade (www.squaretrade.com) is another similar service that I recommend. Tell them KellyCoinGuy sent you.
Several of the traditional coin auction houses such as Superior, Heritage, Cristies and so forth now have online auctions, often through Ebay. I haven't listed these here due to lack of time, and lack of a clear strategy on the part of most of these major auction houses. Sometimes they don't honor bids placed through the Ebay interface, so if you have to have it, call the auction house directly!
Here are a few of the ones I know about. Contact Us if you find another one you want listed or find any inaccuracies on this page.

Coin Specific Auctions

Teletradehttp://www.teletrade.com
These guys have been in the coin auction business a very long time. Long before the Internet was popular, they were auctioning coins over the phone. They still sell coins over the phone, but you can now bid on the Internet as well. This is very good in my opinion as the phones tended to get very busy at the end of the auctions. They have 2 auctions a week with several hundred slabbed coins (that is, encapsulated by NGC, PCGS and Anacs only for now). They have a good search engine, (coin specific) and quite a few pictures. The pictures are for entertainment purposes only unless you are buying expensive coins. They have both buyer and seller fees, and charge a hefty amount for S&H, so be careful, especially on the cheap stuff. A $6 coin ends up costing the buyer around $12.50 and the seller doesn't get anything at that price either. I have bought some nice stuff there though.
Teletrade accepts coins for sale from anyone, but they must be slabbed by a major grading service.
Interesting story. I approached these guys in 1996 about putting their stuff on the Internet (being an Internet computer programmer and a collector). Their response was basically that the Internet was a passing fad, and that they couldn't possibly implement a system on the Internet that was as fair as their phone system, despite the fact that usually you got a busy signal for the last hour of their auctions back then. Well, I guess they finally decided that the Internet wasn't a passing fad, and their system is now much more fair than it was previously. Bottom line, these guys know their coins, but are very conservative about their technology.
Roy Reynolds
http://www.geocities.com/RodeoDrive/7533/auction1.html
Roy has a variety of mostly cheaper coins. I've purchased from him, and the coins were as described. I think they are all his coins. The reserve price is usually such that most coins don't have bids on them, but occasionally you might find something that you really need. He also has an output only mailing list reminding you of his auctions. In this case, smaller seems to be better, as he has outlasted most of the bigger auction efforts. Take home lesson for any would-be online auctioneers -- simple is good.

General Purpose Auctions with Coins

E-Bayhttp://www.ebay.com
And the winner is... Ebay!
The king of online auctions. E-Bay went public, and the rest is history. A quick check usually finds over 100,000 coin lots for sale. Everyone can sell here and everyone can buy here. It requires a little more trust to buy a coin on Ebay because the person on the other end may or may not be a dealer. They may or may not be entirely honest, although there are interesting checks and balances in the system to try and avoid abuses. Only sellers pay fees, which are relatively modest. They offer reserve sales, which set a minimum price, if that is to your liking. There is presently no better place for a collector to sell a coin online. They have now purchased Paypal, which makes paying for things convenient, and adds another layer of safety, especially paying with a credit card through Paypal. You have the guarantee of Ebay, Paypal and your Credit Card company. While it doesn't protect you completely, it does give you a pretty good chance at filing a good grievance should something go wrong.
Beware that many describe Ebay's coin section as "the dumb selling to the dumber." And there may be some truth to this. Coins that I would gradeGood are often listed as VF. You need to know your stuff, and check other's feedback. There are also many counterfeit coins on Ebay. This is especially true for ancient coins, but I've seen bad bust dollars, and many altered mint mark 1916 D Mercury dimes. Anything that might be suspect at a flea market is suspect on Ebay.
One advantage and disadvantage is that they sell EVERYTHING (with a few minor exceptions). The problem with this is that you really have to manually search through a lot of coins to find the ones you are interested in. If you occasionally want to buy or sell other things, then that's great. Since they have the categories, you don't need to look at non-coin items, this is very nice.
I've completed over 400 coin transactions on Ebay myself under the user name KellyCoinGuy. I haven't had a problem yet that wasn't able to be worked out amicably.

Auction Fire

http://auctionfire.com/
Zero coins on this evening (May 2003, Dec 2003). Not highly recommended despite being free. Eventually, I expect they will be in the list below.

Yahoo Auctions

http://auctions.yahoo.com/
Yahoo auctions is a general purpose auction site that entered the game rather late. Initially, they leveraged highly off of the Yahoo brand name, and were interesting competition to Ebay for a while. Tonight they list 7388 US Coins. Not too bad. Although compared to Ebay's 114,842 currently listed items, it's still a little thin.

Amazon.com Auctions

www.amazon.com - Then click on the Auctions tab.
Tonight listing 9127 US coins, a few more than Yahoo, but still far short of Ebay. I couldn't find any coins that had more than one bidder, and dang few had that. As a seller, maybe it's risk free if you start with a high minimum bid. This seems to be what's going on here. For a true auction experience, I'd have to recommend Ebay over Amazon. If you want to try and find something cheap with no competition, Amazon might be a place to occasionally find a great deal.

Coin Sites that don't seem to be Auctions anymore

US Cents.com
http://www.uscents.com/
"All Copper, all the time." This site used to have an auction, and still have an Auctions link, although tonight it isn't active. Perhaps it's only a live link some of the time? I'll give them the benefit of the doubt, and leave the information here. It's a good site whether it still has an auction or not.
This auction has only US copper coins. This does include some tokens and colonials as well. I didn't see a search, but since they normally have less than 100 lots, a search probably isn't necessary. If you are a Copper specialist, this site is worth a visit. With a 2% auction rate for a successful sale, it seems hard to beat financially. However, there is the concern that you won't win as much for your lot as you might if more people saw it. I would suppose also that making money is a secondary concern of the site owners, but I kind of like that since it reminds me of another web site I'm quite fond of. And they are still in business as of January 2004!
SDDCA Auction
http://www.geocities.com/Eureka/Plaza/2660/index.html
Another site that's still active, but doesn't seem to be doing the auction thing anymore. The site is interested only in error coins. If you are an error specialist, this site is worth a visit.

Defunct Auction Sites

With interesting stories to boot. If you are thinking of starting a coin auction site, remember there are a lot of corpses here in the bone yard. Learn from the dead before proceeding.
Numismatists Online (NOL)
http://www.numismatists.com
These fellows used to be the kings of Internet only coin specific auctions (IMHO). However, they have now gone out of business. There were lots of reports as they went down that they weren't paying their seller's the commissions they owed them. If the URL comes back, it will probably be a different group.
Collectors Auction
http://collectorsauction.com/
They are dedicated to collectors in general, but used to do a decent job on coins. They've since gone the way of NOL, although their site is still up, it is now reduced to a bunch of sponsored links. The first one is of course to Ebay.
Coin Universe
http://www.coinuniverse.com/
Again, this used to be an extremely professional web page and Coin Universe was one of the better coin sites on the web. It is now simply a link to the PCGS home page. A good page, but as far as I can tell, not an auction page anymore.
http://auctions.coin-universe.com
This page is apparently still an auction page of some kind, but there are no coins specifically mentioned there.
Williams Gallery
http://www.wgauctions.com
The Williams Gallery had auctions of collections that were consigned to them. They also auctioned their own coins. They also seem to be out of business now.
Coin Auctions of Greater Chicago
http://www.mcs.net/~cagc
Another auction site that seems to have gone the way of the Internet bust, although they busted a bit earlier than most, last known auction in 1998.
Patriot Auctions
http://www.patriotauctions.com
Steve McCabe ran this one. It was nice for a while, and had a great mailing list. Their URL now points to a gun site.
Peace Auction
http://www.peace-auction.com
Another out of business auction site.
Debug Collectables Auction
http://www.debug.ca
Gone with the wind, now a computer company site.
Go Mainline
http://www.gomainline.com/
Used to be a collector centric auction. Now it's just a search page. Too bad, they had some good ideas with a telephony system similar to Teletrade's.

Sell and Trade.com
http://www.sellandtrade.com
Did have a limited coin auction, now is a domain up for sale.
Haggle Online
http://www.haggle.com
Another defunct site that's now a search portal. I never gave them much of a chance.
Box Lot
http://www.boxlot.com/alphadex.htm
Another defunct general purpose online auction. They had a reasonable site, but now it's just a bunch of Japanese.
Up 4 Sale
http://www.up4sale.com
This site had a couple of hundred coin lots when I last checked in 1999. It seemed the same as the others, although there is a tantalizing bit about being free! I suspect they are trying to go with the advertising route to make money. Seems a tough way to do things. (Update: Apparently, Up4Sale was purchased by Ebay in 2000. I would guess that they made some money this way that the other auction sites were unable to make. Congratulations to them, I think it was the best way out!)
Auction Universe
http://www.auctionuniverse.com/
While they once looked pretty good, they are gone now.
Live Auction Online
http://www.liveauctiononline.com
This general purpose auction site had around 100 entries in the US coins section. Now, they are gone.