If your grips are worn out, have become slick and lost traction, have hardened, are leaving dark residue on your glove palms, or are cracking, then it's definitely time to replace them.
Any of those conditions can cause you to squeeze tighter, which inhibits a complete backswing, diminishing swing speed and consistency. In fact, a grip's lifespan can be abbreviated by weather, how frequently you play, any rings on your fingers, or how tightly you hold the club. A general rule of thumb: replace your grips every 40-50 rounds, 30-40 rounds if you’re also spending a lot of time hitting balls at the practice range.
New grips are inexpensive compared to other equipment changes and can instantly improve your game by removing all of your hand tension and thus giving you back control of your swing.