I am a big fan of the band Muse.  They are a British band and began back in 1994.  
What kind of genre are they?
They are a variety of music styles.  There first album really showed off a melancholic alternative rock style.  It was called Showbiz
Hmm.. interesting. Are they grungeish, like Nirvana?
They have a little bit of that.  But they are not as much grunge as the 90s bands of Pearl Jam and Alice and Chains
Who are they most similar too?
One of their albums (Black Holes and Revelations) was compared to Depeche Mode.