A worn out drivetrain will decrease your shifting performance and if not fixed can make your bike unrideable. Your chain and cassette should be checked for wear often, if not replaced you will experience skipping which can send your knee into the stem(ouch). Chain and cassettes usually need to be replaced at the same time as they wear in unison. The front chain rings will take longer before they need replacing since the chain wraps more teeth, there is less stress put upon them. Take a look at the picture below, see how the teeth have been worn down. Imagine a new tooth being a tight U shape, the ones below are a wider u shape and need to be replaced.
Derailleur pulleys can often be overlooked when it comes to replacing parts. Worn out teeth like the ones in the photo below will cause your chain to run rough. It’s very important to have good pulleys as they guide your chain through the derailleur and onto the cassette.