I'll list a few of my favs.
First, I'm really into MAN WITH A MISSION right now. Database (one of the OP of Log Horizon) is a solid song, but I think "Take Me Under," is their best. I'm usually more of a jrock kind of guy, but the current trend over there right now is a bit like the 2008 scene over here, a LOT of seemingly emo/screamo elements that I just do not enjoy anymore. This band is a nice break from that.
My favorite band for good rock music though is Kishida Kyoudan and the Akeboshi Rockets. They've done SEVERAL OPs that you're likely to recognize, but my favorite songs are "GATE" "Strike the Blood," and "LIVE MY LIFE."
You can't go wrong with a little older too. Asian Kung-fu Generation's "Rewrite," and "After Dark," still slap.
Even older than that, Piko's "Kotonoha" never fails to get me amped.
If you're leaning more pop, then Kyary Pamyu Pamyu and Perfume are where it's at. Kyary's "Mondai Girl," and "Kira Kira Killer," and then Perfume's "Secret Secret," are good starting points.
A fascinating pop song is MONDO GROSSO's "False Sympathy" (ft. AiNA THE END from "BiSH") It's a cool song, but the music video is highly suggestive dancing, and I don't often see straight-up sensuality like that in most Japanese music videos.
And lastly, you can never go wrong with BABYMETAL or Nujabes, of course. Bands like The Oral Cigarettes and ONE OK ROCK are also talented rock bands, although, again, they carry a little too much of that middle-to-late 2000s Fueled By Ramen U. S. sound for me.
Another great band that I miss is Maximum the Hormone. Most people know their two songs from Death Note ("What's Up People," and "Zetsubou Billy") but they a cool diversity of sound that make for a fun listen. "Koi No Mega Lover," and "Chu Chu Lovely Muni Muni Mura Mura Purin Purin Boron Nururu Rero Rero Slashkatsu," are both absurd and catchy songs that do not hit quite as heavy as the Death Note ones.