Do not miss this. Even if you're panicking about how high up this place is, don't. I have true vertigo (not acrophobia) and sometimes have issues about where I can or can't go. I managed Corcovado pretty well, so most anyone can. Very wide stone walls around the top keep you from feeling as though you're on the edge.
Take the train from Cosme Velho station. It's a rickety thing, but you travel up through the forest, which is entertaining in itself. Friends who've gone up by car have mainly ended up with vomiting children in the back because of the twisting road.
There are elevators and escalators from the train to the statue itself, so there aren't endless stairs, unless you feel like the penance!
I recommend going either early morning (10 to 11am) or after 3:30pm, when crowds are lighter. There is a decent cafe and souvenir stalls up at the top, and no rip-offs, which is nice! The best photo is from the far end of the top deck, facing the statue. You just have to push your way through to get there!
Be warned that on some holidays, like Christmas and especially New Year's Eve, this place is crazy.