Prostatitis and amplification of undetected existing prostate cancer, and blood clots, are the big two I think? There are minor ones, like decreased sperm count and acne, but people going on TRT probably don't much care about them.

I was told your own body stops producing testosterone and this is permanent. So you are signing up to get injections in your ass once a week for the rest of your life. No idea if this is actually true though, I find it hard to believe personally as many bodybuilders will cycle on and off steroids constantly.