These are obviously only my opnions:
The most common, and potentially most serious injuries are knee injuries (front and/or sides), usually caused by (1) sitting too low, (2) a lack of stretching over a period of time, and (3) not warming up.
Hamstring strains are also common, as are back soreness, and injuries to the back of the knee such as Baker's cyst.
Fat Hack's tips for injury prevention:
Don't sit too low (most important).
Don't sit way too high.
Don't have your handle bars too low, even if it does look cool.
Warm up properly. The more intense your ride is gonna be, the longer you should warm up.
Do some regular abdominal work. All that trunk flexion during cycling, combined with weak abs can really throw the pelvic tilt out of whack over a period of time, which can then cause back, hamstring and other problems down the road.
Stretch regularly, but ONLY when you're warm. Stretching before your ride when you are cold is dangerous and totally unnecessary. The last bit of research I read said that it is important to stretch frequently, but not necessarily before exercise. Don't over stretch -- People do as much harm as good by over stretching. Many people new to stretching believe they have to really "feel" it, so they go too hard.
The main stretches are "the big three": hammies, calves and quads -- then IT Band, lower back, glutes, groin....and if you still have time after all this, feel free to throw in some extras.
Don't be scared to have a couple of days off ocassionally. It's amazing what one day off can do if ride a lot.
Last of all, don't become a big fat hack like me -- it's hard work holding my gut in for a whole ride.