I have had the pill, patch, and shot.
Pill - I took ortho novum for 5 months. I took it at night and wake up in the middle of the night and the room would be spinning, sometimes I would throw up because I was so dizzy. Other times in the morning I would be nauseous and throw up. Many times I tried to go to work hoping it would get better and I would get sent home. Not a good experience. Other than the nausea I had no other side effects. It was hard for me to remember it every day though.
Patch - I switched to this from the pill. Much easier to remember only once a week. I was on it for about seven months before my health insurance ran out. Twice though it became stuck to my skirt/underwear mid week (i wore it on my butt) and once that happens you have to take it off. Sometimes it would shift also and it would have a sticky edge around the patch, I always wondered if it was still 100% effective that way. I had a bit of nausea like sometimes car sickness, nothing as bad as the pill though.
Depo shot - I love the shot! I have been on it for over a year now. Every three months I get a shot in my arm and no period! As long you go for your appointment every three months it is easy. I have had no side effects. When you first start it you may have some spotting between shots. I think it is the most user effective I read because it is a lot harder for the person using it to screw it up (like forgeting to take a pill at the right time.)