If you want to check the number of Backlinks if www.yourdomain.com in google, use this Type the following inside google search box. link:www.yourdomain.com that's it.
If you are using some link manager tool like ARELIS, you should be able to find the websites that link to your website using the option 'Find sites that already link to you'. Also, you can try linkdomain:www.yourdomain.com on AltaVista. For some sites, it will get more results than those displayed by Yahoo!
I use this tool http://www.shoemoney.com/siteinfo.php but seems many tools around will have to be updated with msn live and yahoo siteexplorer
FYI, I wouldn't use google to check backlinks....they only show you a sampling...and they tend not to show your "best" backlinks....and they tend to show some that they prob are not counting (what they show, and what they know, are 2 different things). Altavista is owned by Yahoo, so it's usually similar to yahoo....but I'd trust yahoo a bit more....the drawback to yahoo is that it often shows backlinks that have no google cache (scraper sites)...but it's still better than viewing google's backlinks.
Altavista does show the highest number of links generally .. although many will often be old links that have since been removed. I know this is true in my case because I definitely do not have the 201,000 backlinks reported by Altavista.
try using a tool called RankQuest (rankquest.com), its a good site to use because it has loads of other fancy tools as well. another good one can be found if you type "SEOpen" into Google. Thats a handy tool to use. you can just right click on sites and analyse them using all sorts of tools. hope this helps.
You can also check with linkdomain:domain.com -site:domain.com You are probably new in SEO industry. Getting backlinks is the most effective way to boost your rankings.
I use many tools to check my backlinks. If you can offord it SEO Elite is awesome! But another tool is use is Link Popularity Check, and it is FREE. You can find it here: http://www.checkyourlinkpopularity.com No, I am not affiliated, but I use their tool often. It downloads to your computer so you can use it easily. The only problem is that they try and sell Arelis on some of the tabs in the tools. They also have great articles written for webmasters. Awesome information.