I'm really surprised no one mentioned Laruku yet. Well, my favorites are:
Asian Kung-fu Generation: relatively new band. I love the kind of music they play (something like punk rock). All their songs are awesome, but I'd say my favorites are Song of Blue; Kimi to Iu Hana; Natsu no Hi, Zanzou; Sunny Day and Compass. People may know them by their song Haruka Kanata, which was the song used for Naruto's second opening.
Laruku (L'Arc~en~Ciel): pretty much my favorite Jpop/Jrock band ever. I like the majority of their songs, Hyde's vocals are perfect. Their style varies all the time- heavy songs (like The Nepenthes) to slow ballads (like Winter Fall) which are my favorites. I like almost all the songs, but I'd say my favorites are Winter Fall; Stay Away; All Year Around Falling in Love; Driver's High; Ibara no Namida; Ready Steady Go; Love Flies; Neo Universe; Perfect Blue; Time Slip and Spirit Dreams Inside
Hyde: I'd also like to mention Hyde's solo carrer, which I like very much too. The songs are a heavier than Laruku (his solo carrer is kind of japanese heavy metal), but they're awesome. His 666 solo album is just perfect. My favorite songs would be Fruit of Chaos; Hello; White Song and Shining Over You.