Is there any particular kind of rock or metal this topic discusses? Metal is an umbrella term, underneath the giant umbrella term rock. Rock in general is most of the music I like, and in just about any kind of rock. There are hundreds of rock bands that I like. As long as everyone's doing their top ten lists, might as well make mine.
1. Linkin Park: My favorite band of all time. I've been listening to them since 2001, when they're first album, Hybrid Theory was released. I guess I like all of their albums, but the first two were amazing while the fourth was disappointing. I would consider them Nu-Metal or rap-rock.
2. Three Days Grace: Great to listen to, love all three of their albums. Emo-metal.
3. Depeche Mode: Might be considered techno, but think of them as a hybrid between techno, pop, and rock. Very deep music, good for thinking.
4. Papa Roach: Well, their early albums. There's no way to justify how great they were. Were nu-metal/ rap-rock, now emo.
5. Red Hot Chilli Peppers: Do I need to explain this one?
6. Nine Inch Nails: Techno-y rock. Deep lyrics. And they're original version of "Hurt" is so much better than Cash's cover.
7. System of A Down: Trailblazers for screamo. Some of their songs are a little too intense for me, but most are good jams. Serj Tankian's voice is just great.
8. Audioslave: This should be further up the list, but I'm too lazy to change the numbers. Chris Cornell's voice is absolutely amazing. Take him and put him with Rage Against the Machine (without Zach de la Rocha), and you've got an amazing alternative rock band.
9. Pink Floyd: Just got into them, actually. Nice, calm rock.
10. Muse
I like some of the others mentioned, too, like Evanescence and Oasis. However some bands that are incredibly famous, I don't like that much. Like Nirvana or Foo Fighters.
I also like all of those 90s grunge and post-grunge bands like Alice in Chains, Soundgarden, Counting Crows, Candlebox, REM, Sponge, etc., etc.