This band broke up in 2013, but there's no chance of a reunion now, because Wayne Static (frontman of this band) died of an overdose a year ago. They made a lot of good music together. While not technically broken up, this band went on hiatus in 2010 to focus on side projects, one of which being Hellyeah. Do you have any bands you like that broke up but wish still performed together?
Guns N' Roses is the first that comes to mind. Almost no chance of a reunion there, what with Axl Rose having become a big fat a-hole. Spoiler: Welcome To The Jungle Spoiler: Sweet Child O' Mine
If you can include break ups due to death: Bathory Death Lifelover Emperor Impetigo Reverend Bizarre Strapping Young Lad
Got some more here. This band released one album in 1997. They could have been big, but the band's vocalist (Shannon Crawford) decided he wanted to pursue a solo career instead. As such, they split up. This band released two albums in 2001 and 2003. Their debut album One Nation Under was well-received by critics, but did not do well commercially despite the posted song's airtime on radio and TV. They had a third album in the works, but most of the band were consumed by their day jobs, resulting in the album being scrapped and the band breaking up in 2005. Shame really; their music was really good, even if they (or the singer, at least) look like a dollar store Mudvayne. While not technically broken up, this band went on a hiatus in 2012, but briefly reunited in 2014, only to go into another hiatus. So far, they have released seven albums, the latest of which being released in 2011. Right now, vocalist Aaron Lewis is undergoing a solo career and has released an EP and a studio album, while guitarist Mike Mushok is performing with Canadian supergroup Saint Asonia alongside former members of Three Days Grace, Finger Eleven and Stereomud. I don't think I need to say anything about this band...
A few bands who had broken up but are getting back together that I'm psyched about are Xandria and Neuroticfish. As for bands who have broken up that I want to see return, those would be System of a Down, Nirvana, and Manmade God.
Feel ya on that one. They still play shows on occasion, but I'd love to see them record a new album; it's been over ten years!