Birdman and The Grand Budapest Hotel lead the race for this year's Oscars with nine nominations each.
The Imitation Game, Boyhood and American Sniper also have multiple nominations.
There was good news for British actors as Benedict Cumberbatch, Eddie Redmayne, Rosamund Pike, Felicity Jones and Keira Knightley are all nominated.
Up against Cumberbatch and Redmayne for best actor are Steve Carell, Bradley Cooper and Michael Keaton.
Cumberbatch, who plays codebreaker Alan Turing in The Imitation Game, said he was "knocked for six" by the nomination.
"So excited and honoured to receive this recognition," he said.
"It's wonderful to be included by the Academy in this exceptional year of performances. To ring my parents, who are both actors, and tell them that their only son has been nominated for an Oscar is one of the proudest moments of my life."
Fresh his Golden Globe win on Sunday, Eddie Redmayne, again nominated for his role as Stephen Hawking in The Theory of Everything, told the BBC how he heard the news in Los Angeles.
"It's the crack of dawn and I've gone from being in a deep dark sleep to hearing this news. I can't quite articulate what I'm feeling but I feel pretty good".
He played down any rivalry with his "old friend" Benedict Cumberbatch, calling him a "lovely, wondrous, human being".
"We've been texting this morning and there have been a lot of exclamation marks of euphoria so there's definitely no competition there," he said.
Redmayne revealed he would stay up to watch the Oscars as a child but would "never ever dream I'd get to go. Frankly being invited to the party is an extraordinary thing".
Meet the Oscars nominees
It is Bradley Cooper's third consecutive Oscar nomination in the best actor shortlist, this year for his role in Clint Eastwood's military biopic American Sniper.
He is the first actor to achieve this feat since Russell Crowe was nominated for The Insider, Gladiator and A Beautiful Mind at the start of the century. He won for Gladiator in 2001.
Meryl Streep is nominated for her 19th acting Oscar, breaking her own Academy Awards record. She is up for best supporting actress for Into the Woods alongside Knightley, Patricia Arquette, Laura Dern and Emma Stone.
Nominated alongside Felicity Jones and Rosamund Pike in the best actress category are previous Oscar winners Reese Witherspoon and Marion Cotillard, alongside Julianne Moore, who recently won the Golden Globe for her role in Still Alice.
Those who missed out in the category included Jennifer Aniston, who was nominated for a Golden Globe for her role in Cake, and Amy Adams who won the Golden Globe for best actress in a musical or comedy for Big Eyes.
Speaking immediately after the announcement, Felicity Jones, nominated for her role as Stephen Hawking's first wife Jane in The Theory of Everything, admitted she was too nervous to watch the nominations live.
"It's so nerve-wracking I couldn't watch it", she told BBC 5 live. "I was just waiting and I got a phone call from my brother. He was very sweet, he just said: "you've done it, you've got it.
"I was just so excited. It's one of those things you never quite expect. It's just fantastic news".
The nominees in the main categories are:
- Wes Anderson (The Grand Budapest Hotel)
- Richard Linklater (Boyhood)
- Alejandro G Inarritu (Birdman)
- Morten Tyldum (The Imitation Game)
- Bennett Miller (Foxcatcher)
- Steve Carell (Foxcatcher)
- Bradley Cooper (American Sniper)
- Benedict Cumberbatch (The Imitation Game)
- Michael Keaton (Birdman)
- Eddie Redmayne (The Theory of Everything)
- Marion Cotillard (Two Days, One Night)
- Felicity Jones (The Theory of Everything)
- Julianne Moore (Still Alice)
- Rosamund Pike (Gone Girl)
- Reese Witherspoon (Wild)
Robert Duvall's nomination for best supporting actor in The Judge makes him the oldest Oscar nominee in this category. At 84, he is two years older than the previous oldest nominee, Hal Holbrook, who was up for Into the Wild in 2008. The oldest winner in this category is Christopher Plummer, who was 82 when he picked up the Oscar for Beginners in 2012.
The Lego Movie was a surprise omission in the best animated film category, although its catchy theme song Everything is Awesome, by Tegan & Sara, is up for best song.
Also up for best song is Grateful written by Diane Warren and performed by British singer Rita Ora in Beyond the Lights, alongside John Legend, who won the Golden Globe for his song Glory from the film Selma.
Civil rights drama Selma's only other nomination comes in the best picture category.
The live action short category includes The Phone Call, by British director Mat Kirkby, in which Sally Hawkins plays a helpline call centre volunteer who counsels a mystery man.
The film was shot in 2013, a week after Hawkins finished filming Woody Allen's Blue Jasmine (for which she was nominated for the best supporting actress Oscar last year). Kirkby sold his car to pay for the film.
Also in the live action short category is Boogaloo and Graham, directed by Michael Lennox. Filmed entirely on location in Northern Ireland, the film is set in 1970s Belfast and follows two young boys who discover the facts of life, aided by the help of their pet chickens. The short also picked up a Bafta nomination last week.
The nominations were announced in Hollywood by Alfonso Cuaron, who won best director for Gravity last year, alongside actor Chris Pine, Star Wars director JJ Abrams and Oscars boss Cheryl Boone Isaacs.
Television and film actor Neil Patrick Harris will host the ceremony in Hollywood's Dolby Theatre on 22 February.
You can keep up to date with our live feed of the Oscar nominations and reactions as they happen.