As mentioned by @gev, Bricklink is a great place to go. It is, however, not the most intuitive site to use. Here is how you can easily get the item counts:
- Start with the Search box at the top of the page. Before typing in the name of the set, make sure the selector is set to search the Catalog.
- Enter a term from the name of the set (e.g. "Millenium" or "Falcon").
- The Catalog results will pop up. You might find sets or individual pieces listed, or even several (regional) variations on the set.
- Go to the entry that best describes the set you (think you) have. The entry will start with a number (e.g. 10179-1 for the Millenium Falcon UCS) and after the number, in parenthesis, you will find a link to the inventory (labeled "(Inv)"). Clicking on this link gets you to a detailed inventory with item counts for the particular set.
Rinse and repeat for other sets you have ... good luck!
Alternatively if the set is from 2002 or later, you can go to http://service.lego.com/en-us/buildinginstructions to download the building instructions, which contain a detailed inventory at the end. Unfortunately, the resolution and color palette of these instructions is not the greatest (at least on the ones I've tried) so it might require some sleuthing to decipher the different pieces (studs are not showing very well, and it is difficult to tell the different color shades apart, like light grey, dark grey and black).