Adele is up for six Grammys including song and record of the year, for Rolling in the Deep, and best album, for 21.
Rapper Kanye West leads the field with seven, while Bruno Mars and the Foo Fighters also have six each.
Mars, also up for best song, record and album, said: "It feels incredible."
British band Radiohead are up for five awards including best rock performance and song for Lotus Flower. Winners will be announced on 12 February.
Lotus Flower is also up for best short form music video - against Adele's Rolling in the Deep - while the band's The King of Limbs is nominated for best alternative music album and best boxed package.
They will compete for best rock performance and best rock song against Every Teardrop is a Waterfall by Coldplay, who are also recognised for the track Paradise.
Their song goes up against Body and Soul, a duet by Tony Bennett and the late Amy Winehouse, for best pop duo/group performance.
Fellow Britons Mumford & Sons have four nods, including in the record and song of the year categories, for The Cave.
The folk four-piece, nominated for best new act at the 2011 Grammys, performed The Cave at February's ceremony.
Adele, whose second album 21 is currently the best-selling record in the US this year, is also nominated for best pop solo performance, for Someone Like You.
Briton Paul Epworth and Ryan Tedder, who produced tracks on 21, were both nominated for the non-classical producer of the year gong.
Adele, who is recovering from throat surgery, won two Grammys in 2009 including best new act.
Other British acts who received a nomination included Corinne Bailey Rae, Jeff Beck, the BBC Philharmonic with conductor Sir Andrew Davis, and Susan Boyle - nominated in the best traditional pop vocal album category, for The Gift.
Kanye West, whose My Beautiful Dark Twisted Fantasy missed out on an album of the year nomination, is up for song of the year, for All of the Lights, which features guest vocals from acts including Alicia Keys, Elton John and Rihanna.
Most of his remaining nominations came in the rap categories.
Also competing for song of the year are Bruno Mars' Grenade and Holocene by US folk band Bon Iver, who have four nominations.
Mars said he was particularly thrilled to be recognised for Grenade.
"That's the song we worked the hardest on - that's like our trophy right there," he said.
"Of all the songs we've been fortunate enough to be a part of this year, we were most proud of that one."
Bon Iver's Holocene is also up for record of the year - which honours the composers of a song - as is Mars' Grenade and Katy Perry's Firework.
For album of the year, Adele's 21 goes up against Foo Fighters' Wasting Light, Lady Gaga's Born This Way, Rihanna's Loud and Mars' Doo-Wops & Hooligans.
However, there was no nomination in that category for previous winner Taylor Swift's Speak Now.
Swift, who did get three nominations including for best country album, won the prize in 2010 with Fearless.
Rapper Lil Wayne and dance music producer Skrillex have five nominations each.
Skrillex - real name Sonny Moore - competes against Bon Iver, hip-hop artist J Cole, rapper Nicki Minaj and country act The Band Perry for best new artist.
Nominations were announced during a televised concert at the Nokia Theater in Los Angeles featuring performances from acts including Lady Gaga, Katy Perry and Nicki Minaj.
Winners will be announced at the 54th Grammys in Los Angeles in February, in an award ceremony that now has been reduced to a total of 78 categories compared with 109 last year.
The cull, which provoked some protests, eliminated more niche categories and pared down vocal categories for pop, R&B and country, which previously had male and female winners.