Yahoo Site Explorer is the easiest and most accurate way right now. Go to: http://siteexplorer.search.yahoo.com/advsearch?bwm=i&bwmf=s&bwmo=d&p=http%3A%2F%2Fyourdomain.com and replace "yourdomain.com" in the url with your site's domain. You can also use this tool: http://www.webmasterlogs.com/link-analysis-tool/backlinks.html
In Google check your back links, link:yourdomain.com In yahoo check your back links, site:yourdomain.com
for Google: link:yourdomain.com or link:www.yourdomain.com Yahoo: linkdomain:yourdomain.com or linkdomain:www.yourdomain.com
This is my favorite, you can also check teh pr of your backlinks too, it seems to be more accurate than any other backlink tools.
I have found the Google backlink checker to be inaccurate.. The Yahoo siteexplorer seems to be the best way ahead.
Yeah, i use Site Explorer as well. Besides there is a plugin for Firefox which allows to see PR's of backlinks listed.
If you want to see how popular your site is, use the following search phrase at Google: yourdomain.com -site:yourdomain.com That phrase will show all pages where the html code contains "yourdomain.com". Be aware that it will return more results than just backlinks. If a page hotlinks to one of your photos, it will be listed. So will pages that mention your site without linking to it. So will sites that link to your site using a "nofollow" link.
Small adjustment to MrTampaFL suggestion put a + plus sign in front of your domain when doing that search +example.com This is far more accurate for finding references to your domain in Google's index. Don't forget to monitor the referrers in your statistics reports.
Found this site on DP earlier, I like it alot so far http://seopro.com.au/free-seo-tools/link-checker/
I Wrote a post on my blog with tons of different resources for finding how many backlinks your site has: How To Check How Many Backlinks Your Site Has Hope that helps... it has a few of the links people have provided here, and some others.