A loose faucet handle will gradually grind away the valve stem that it's screwed to, and should be tightened. Here's a trick to use if the stem is already badly worn.
By the DIY experts of The Family Handyman Magazine:December / January 2006
Add more years of life to a worn plastic valve stem by wrapping it with Teflon plumber’s tape.
If you have a loose valve handle—on a shower, bathroom or kitchen faucet—tighten the screw that holds the handle in place. With some faucets, you'll have to pry off the metal button at the center of the handle. With others, you'll find a setscrew near the base of the handle. Setscrews usually require a hex (or “Allen”) wrench. If tightening doesn't work, the stem inside the handle may be worn, especially if it's plastic. Here's a trick to tighten worn stems on most types of faucets: Wrap the stem tightly with Teflon pipe thread tape and slip the handle back over the stem. In most cases, a single wrap creates a snug fit.
Have the necessary tools for this DIY project lined up before you start—you’ll save time and frustration.
Avoid last-minute shopping trips by having all your materials ready ahead of time. Here's a list.