Is there a way of using something like as a search engine to find out which web sites out there link to mine?
In google type:
Also their webmaster tools will give you a better rundown. Bing also has webmaster tools.
It's pay-for-play, but SEOmoz recently released their "Open Site Explorer" tool which analyzes backlinks, (amongst other things) as well.
http://developer.yahoo.com/search/siteexplorer/ is much better than using "link:yoursite.com" in Google search.
The 1st one will give you a much wider list of links to your site. Google "link:yoursite.com" used to give you many results too, but after they did some changes on it and now is returning nothing compared to what site explorer returns.
Unfortunately Microsoft took over Yahoo and there seem to be plans to turn siteexplorer off soon: "The Yahoo! Site Explorer team is planning tighter integration between Site Explorer and Bing Webmaster..."
Try www.backlinkwatch.com it mines the search engines for backlinks to you and shows you the results with pagerank values attached.