I like classic metal, if you want to call it that. The heaviness that I like, if it suits the song, than great, if not... well does it sound good?
For metal, I like Metallica, Sabbath, some Slayer, Alice in Chains the list goes on. As long as the song has something memorable about it, I tend to like it.
Also, I'm a huge fan of Coheed and Cambria, and while they aren't metal, I love how they have a variety of "flavors" in their music, and still have a unique "taste". Welcome Home, by them is a pretty heavy song, whereas A Favor House Atlantic, or Blood Red Summer, are much lighter.