Do cartridges wear out? How can you tell? I know a stylus can wear out because it is in contact with the record but the cartridge is not.

They shouldn't.

Needles yes.

I've had a Shure V15typeIII for close to 30 years now.

Do cartridges wear out? How can you tell? I know a stylus can wear out because it is in contact with the record but the cartridge is not.

Generally speaking only if you get them near a magnetic source (magnets = death for cartridges) or if a winding shorts / goes open. Usually a cart fails due to abuse or mishandling.
Common cartridge failures include: one side louder than the other, one side dead, hum that can't be traced to the turntable wiring, low output volume or no output volume, stylus shank too loose or crooked in cartridge body, etc. Some of the abuse I've run across include: physical damage such as the body being torn apart when disconnecting the wiring clips, someone making the mistake of soldering the wires to the cartridge pins instead of using the proper connectors and destroying the windings, incorrect stylus shank jammed into the cartridge body, using a cheap voltmeter to measure the coil resistance and damaging the windings, exposure to magnetic fields, f***ed up stereo epuipment that sends damaging voltage through the pickup leads (caused by people grounding the turntable to the house ground rather than the chassis of the receiver) just to name a few. Beware of buying used cart bodies from strangers, you never know what's been done to them over the years!:sigh: