Which home improvement projects produce the highest return on investment when selling?
Having sold a home last year, I can say based on recommendations from our Realtor and the feedback we got from showings...

The BEST thing you can do is to declutter your house.

First, scout out a local storage unit. Get a 10'x10' unit or bigger (we had two). You'll use lots more space than you'd think.

Then, start filling it:


Pack up all clothing you won't be wearing during the time you're selling (out of season clothes, stuff that doesn't currently fit, out of style, etc.). Even things hanging in closets; people will see all the unused space (where you removed things) and see it as much bigger when empty. If your closet is packed with stuff, it'll look tiny.
Pack up your linen closet (except for a couple extra sheets, towels, and blankets). Most people accumulate way more than they'll use. Leave an item or two on each shelf, max.
Pack up most/all knick-knacky things from counters, shelves, etc. that are in normal view around the house. Many Realtors will tell you to remove photos of your family/friends as well -- it helps potential buyers to visualize THEIR family there instead of yours.
Pack up kitchen utensils, pots, pans, etc. that you don't use often. 
Pack up all the holiday decorations (from garage, basement, attic, etc.) you won't be using this spring. 
Within reason, try to remove a piece of furniture from each room. Especially things like that extra lamp, chair, couch, or end table you couldn't part with and just found somewhere to keep it. 


Feel free to donate or sell items instead of storing them.

Also use the occasion as a chance to get rid of any expired food from the back of your pantry shelves or fridge. If you have storage shelves in your garage or basement, getting rid of old paint cans, yard chemicals, scrap lumber, etc. is also a good idea (do NOT put them in a storage unit).

If you're still motivated to do a project or two, continue with these cheap projects that make a big impact:


Paint rooms. Tend to go for an off-white neutral color. Also, use the same color on all the walls; don't use an accent color on one wall. Bold colors or accent walls can be extremely polarizing as people either love them or hate them and typically have a hard time envisioning a room in a different color. As @Tester101 mentioned in a comment (and other answer), you may want to avoid bright white.
Get any stains out of existing carpeting.
Make sure all window blinds are in good condition. If they're bent, broken, or extremely faded then replace them.
Wash your windows (inside and out).
Repair any screens that have holes.
Remove any hard water deposits from your sinks and tubs (CLR works great for this).