How do I check who links to me?
link:www.mydomain.com
You may also want to download the Google toolbar to make are your link checking quick and easy :)

How do I check who is linking to my competitors?
The same way. insert evilcompetitordomain where mydomain was.

Want to save time? Quick tip worth a quarter: Many sites have a single large link partner which makes it hard to view the other links going into that website. In Google's search results they cluster documents from the same site. You can quickly scan most of a websites backlinks by increasing the # of search results appearing on the SERP.

A typical google search string looks something like this

http://www.google.com/search?sourceid=navclient&ie=UTF-8&oe=UTF-8&q=adsense

Inserting &num=100 at the end of the search string will increase the results showing on the page to 100. Your search string will look like

http://www.google.com/search?sourceid=navclient&ie=UTF-8&oe=UTF-8&q=adsense&num=100

This will make link scanning super duper quicker...thus it is worth a quarter :)