In what order should I watch the films in the Marvel Cinematic Universe?
The full chronological (not release order! I assume you're asking for chronological, as release order is easy enough to find on Wikipedia) order, bolded the ones that interest (and/or should) you:
Captain America: The First Avenger (Film)
Agent Carter (One-Shot on the Iron Man 3 Blu-Ray)
Agent Carter (TV series)
Iron Man (Film)
A Funny Thing Happened on the Way to Thor's Hammer (One-Shot on the Captain America: The First Avenger Blu-Ray)
The Incredible Hulk (2008 Film)
Iron Man 2 (Film) (Hulk's campus rampage can be seen in the background)
The Consultant (One-Shot on Thor Blu-Ray)
The Avengers (Film)
Item 47 (One-Shot on The Avengers Blu-Ray)
Iron Man 3 (Film)
Agents of SHIELD (TV Series: Season 1, Episodes 1-7)
All Hail The King (One-Shot on the Thor 2: The Dark World Blu-Ray and digital release)
Thor 2: The Dark World (Film)
Agents of SHIELD (TV Series: Season 1, Episodes 8-16)
Captain America: The Winter Soldier (Film)
Agents of SHIELD (TV Series: Season 1, Episodes 17-22)
Guardians of the Galaxy (Film)
Daredevil (Netflix Series)
Agents of SHIELD (TV Series: Season 2, Episodes 1-19)
Avengers: Age of Ultron (Film)
Agents of SHIELD (TV Series: Season 2, Episodes 20-22)
List taken from this source. The list was compiled based on clues and/or direct references made between movies and/or info released by creators. I've changed it a little, as the original list was a little inaccurate.
Note that some films are likely happening simultaneously - like Iron Man and The Incredible Hulk.
Tony Stark's organisation sold anti-Hulk weapons to the army (that had to happen before Tony returned from captivity), and yet at the end he approaches the General with the Avengers initiative as a solution to Hulk (after finishing his first bossfight as IronMan).
Hmmmm... what's the justification behind watching Ant-Man before the rest of SHIELD season 2?