I was just in Rio de Janeiro in February. Brazil is an absolutely amazing country. First, what you need to be aware of. I think people make Rio out to be more dangerous than it is, but nonetheless, you need to be careful. Brazil attire is very casual - shorts, t-shirt, and flip flops. NO flashy anything - absolutely NO watches, earrings, rings, bracelets, necklaces, etc. Also, don't walk around with your wallet, camera, ipod, or other royalties out in the open. You're just asking to get jumped and you will. Be especially careful near the favellas and close to the beaches.
Great things to go see...
1) Christ the Redeemer - I'm Jewish and it was one of the most incredible things I've ever seen. It's HUGE! You take a tram up a steep mountain, which is quite pretty itself, and then the Jesus stands at the top of the mountain overlooking the entire city. It's a phenomenal view of the entire city of Rio from the top of the mountain. Religion aside, it's symbolic because people view the statue as the protectorate of the city, watching over them from above. A must see.
2) Sugar Loaf - this is a series of two separate mountains that extend out into the harbor from the mainland. You can either take a tram up the first one or hike it. I suggest hiking it. It looks daunting but it's definitely doable and very beautiful. Then you have to take a tram to the second mountain. From the top, there is an incredible view of the entire city of Rio. Again, a must see.
3) Soccer - if there is a game while you are there, GO! It's one of the coolest and most unique experiences I've ever had. It's pretty crazy but a lot of fun and definitely worth it. But if you go, be especially careful at a venue like that. The game I went to is below.
4) Capoeira - if you're able to have a cultural experience with this, it's really cool. Capoeira is a Brazilian mixture of martial arts, games, and dance. It was created by the slaves and they used it as a defense mechanism if their owners caught them attempting to escape. But if they were caught practicing the martial arts, they turned it into a dance so their owners wouldn't know what they were actually doing.
5) Beach - a lot of people go to the Copacabana. Don't be a stupid American tourist and think that the Copacabana was named after Barry Manilow's song or vice versa; it was for a night club in Miami called "Copacabana". Anyways, Copacabana is very very touristy and overcrowded. I would suggest going to Ipanima beach, which is just around the corner from Copacabana. It's a little less touristy but absolutely beautiful. Use lots of sunscreen because the sun is especially hot there. You'll fry like a lobster.
6) Samba - go to an authentic night club and dance your ass off.
7) Beef - eat a lot of it. It's some of the best in the world.
Can't think of anything else off the top of my head. Have a great trip.