I'd wait a good six to eight weeks for each lobe piercing, and much longer for a cartilage piercing. Cartilage does not have a direct blood supply, so takes FOREVER to heal fully (and the risk of infection is much higher, even if you take good care of it).
Try not to touch fresh piercings with your fingers, unless they are just washed. Keeping your hair away from them helps too, if possible. What DonnaF says is true. You may well not get an infection, but if you do, it can be very serious, very quickly. And even if you don't lose your life, it could leave your ear mutilated. Sometimes, after the ear swells up dangerously, the cartilage somehow gets attacked and can be destroyed, leaving you with half an ear.
Having said that, I currently have five ear piercings, all of which have small but chunky silver rings in them. I've had up to seven, but a couple have grown in. I never did adjust to the one cartilage piercing I had (in my early 20s); I found it uncomfortable to sleep on, even after it was fully healed, and even with a ring, not a stud, in it. After a year or so, I let it grow in. Same with the only body piercing I've ever had -- that one never healed properly, which was my own fault because I let a friend do it with a suture needle from the animal lab. (Don't do that!)
