For the sort of coins you see in big name auctions ACSearch is a good paid resource or CNG archives if you don't want to pay. For lower value coins look at eBay sold listings. That said prices fluctuate a lot depending on venue, time of year, rare styles/varieties and a whole host of other factors that are sometimes hard to understand. It's not at all uncommon to see a coin sell for half or double what a similar or even the same coin sold for a year ago. My advice is to look at prices sold for similar coins and try to figure out what a coin is worth to you rather than constantly hunting for a bargain as some collectors do. For the most part I don't regret when I get outbid on coins that are common enough that I can bid on a similar one again next month but I still kick myself for not bidding more on some truly special coins where I focused more on what similar coins sold for than how much I wanted the coin and how much it would have been worth to me.
I heavily rely on coinarchives.com, which has all the major auction results from the last 6 months-year. If I'm looking for rarer coins I use acsearch.com. acsearch has listings dating back around 15 years, but they don't tell you the price, unless you pay. However if you search the particular auction, and it has been in the last five years, chances are you can find a results sheet from the auction houses' website, and then cross check the lot number. Sixbid and biddr also have archives but these are hard to browse from the sites. Instead, google the auction you're looking for with the date and either sixbid or biddr and you will *probably* find the auction archive. I also use CNG's sold lot archive. Keep in mind that the prices listed on all these sites don't include the buyers fees, which are often quite substantial, ~20%. It's also useful to look at the estimate vs. price realized. Often times the estimates on these sites are artificially low to encourage bidding. It's also useful to note when a lot goes unsold what the starting price was. Lastly for more common coins you can search on vcoins and ma-shops and ebay to see what other sellers are charging. I find it difficult to use the sold lot archives on these sites, so I rarely try. If you're looking for a coin that maybe a lot more commonly sold in one country than another (say a taler in germany or a papal coin in Italy or a Tudor coin in the UK) look at that country's version of ebay to see if they sell for a very different sum, there. Just including international sellers on a regular ebay search will miss a lot of listings.
I use acsearch. I think the access to prices is well worth the cost of the subscription. I also use CNG and coin archives.