I've got some experience with old audiocassettes and I can recommend several things.
1) Get a really good-quality tape player. If you're using a generic cassette player, such as a Walkman or a battery-operated unit, it may not have enough motor torque to overcome the tape's tension.
2) Cheaper brands of recording tape tend to get sticky with time. You may notice this if you look very closely at the cassette with a flashlight as it's playing: the tape doesn't easily peel away from the supply reel... it tends to "hesitate" in pulses, adding drag and audible "wow."
3) Cheaper tape players can't read an audiocassette if the felt pad is missing. Better-quality tape decks can.
4) Very old reel-to-reel tapes are often literally baked in ovens to prevent the magnetic material from shedding off of the plastic base during playback, but this is the sort of thing done only as a last resort and done simply to "bump" the audio to more modern media. Until this discussion thread I'd never heard of anyone doing it with an audiocassette, but it's simply a reel-to-reel tape in a plastic shell.
5) Giving the audiocassette a couple of hard "whacks" against a table or even dropping it onto the floor from a couple of feet may help. Seriously. This is sometimes a good temporary fix.