I like LP and 30STM but LP is in no way unique, and 30STM is conceptually overblown.
BATS is an Irish group that fuses post-hardcore, metal, and mathrock, almost always with groovy rhythms and quirky scientific or historic lyrics, being dubbed "nerd-rock." I find these guys really fun, and while musically they're not the most unique thing in the world, their particular brand of rock is entertaining and interesting. The lyrics drive BATS' songwriting to another level.
Dredg is an American band known for their concept albums, most of which featuring Gavin Hayes' beautiful vocals and post-rock, art rock and prog rock influenced songwriting. Take a listen to El Cielo, an album blending themes of sleep paralysis, art in the 21st century, and 'Dream Caused by the Flight of a Bee around a Pomegranate a Second Before Awakening by Salvador Dali,' and you just float off to another world. Their latest efforts have been decreasing in quality but they've still got the goods live and I envision them releasing something else great before breakup.
Blue Man Group. I don't care that the music itself isn't particularly original. The way that they go about everything they do is just so bizarre and fun and carefree and entertaining, it doesn't matter.
Icelandic group Sigur Ros are a forerunner of the post-rock genre, with ethereal vocals and often times long, drawn out and ambient compositions. This style has been copied many times since, but Sigur Ros' spin on post-rock and their true passion towards music is evident and trumps all competition in that category. Their lyrics on ( ) and a few other tracks are in the made-up gibberish language Hopelandic (Vonslenska), and can be interpreted any which way. Pretentious? Yeah, a bit. Awesome? Obviously.
While the Australian group Snowman broke up two years ago and no longer tours, I feel the need to sidestep that criteria, as they're still recent and are easily the most unique group I've heard. Snowman's music is ghostly and haunting in a way that I don't think has quite been captured as eloquently as how they do it: shimmering falsetto and group vocals with tribal and industrial percussion rhythms and songs delayed with lots of reverb. It's a very freaky immersing experience when listening alone in any setting. This is goosebump-inducing stuff that will chill you, and every second is incredible, unique, and unlike anything other.
Those are my top 5.
Wow, two thumbs down?
Oh that's right, I forgot people always vote down things they don't know.
Pardon me for writing these little summaries and giving quality over quantity.
Next time I'll stick with some generic run-of-the-mill mainstream rock to please the masses.
God forbid I actually answer the question.