I'm personally more of a fan of the DCEU, but I do enjoy the MCU films. That said, of the 13 MCU films to date, only about half are essential (meaning that they contribute to a coherent, linear story). The MCU is essentially the stories of <PERSON> and <PERSON> and how they gradually interconnect into the Avengers films. So here are the ones that are the connective tissue that hold the narrative together:
1. Iron Man
2. Iron Man 2
3. Captain America
4. The Avengers
5. The Winter Soldier
6. Age of Ultron
7. Civil War
Iron Man starts everything off, establishing <PERSON>, alluding to <PERSON>, and introducing SHIELD.
Iron Man 2 establishes the greater Marvel Universe by giving us a proper introduction to <PERSON> as well as <PERSON> and <PERSON>. It also hints at the <PERSON>, <PERSON>, and <PERSON>. It also gives us our first real look at <PERSON> in a newsreel intro.
Captain America gives a proper introduction to the title character, lays the foundation for how SHIELD was created, introduces HYDRA, and gives us more background information on <PERSON>. It also introduces <PERSON>, one of the founders (with <PERSON>) of SHIELD. <PERSON> is also introduced (which eventually leads to Winter Soldier).
The Avengers brings everything together: <PERSON>, <PERSON>, <PERSON>, <PERSON>, and SHIELD, and gives us a proper introduction to the <PERSON>, <PERSON>, and <PERSON>. <PERSON> is also introduced. 569
It's not necessary to have seen the <PERSON> and <PERSON> solo films as they don't really add any information that is relevant to the ongoing narrative.
The Winter Soldier gives us more background on <PERSON>, SHIELD, and HYDRA. It also further develops Black Widow. <PERSON> is introduced. SHIELD falls, and HYDRA's overarching plan is revealed. <PERSON> is introduced as is Winter Soldier. <PERSON> is shown at the end of her life.
Age of Ultron builds off of the fall of SHIELD, introduces <PERSON> and <PERSON>, and also introduces <PERSON>. Sokovia and Wakanda are also introduced. <PERSON> and <PERSON> join the Avengers.
Civil War builds off of the stories in Avengers, Winter Soldier, and Age of Ultron (the events in each triggered the Sokovia Accords). Ant-Man, <PERSON>, and Black Panther are all formally introduced. Wakanda is fleshed out more. Crossbones attacks. More background is given on <PERSON>. All of the interconnecting threads tying together <PERSON> and <PERSON> finally come together (and clash). <PERSON> dies.
Thor 2, Iron Man 3, Guardians of the Galaxy, and Ant-Man don't really add anything to this central narrative and can be ignored, although the first scene of Ant-Man set in SHIELD headquarters in 1989 with <PERSON>, <PERSON>, and <PERSON> is pretty cool. Ant-Man's origin is otherwise as unnecessary to the narrative as Black Panther's and Spider-Man's were for their introductions.
Based on all of this, I'm guessing that the only other essential MCU films to come will be the next two Avengers films (Infinity War and the as yet untitled Avengers 4). That would give a total of nine necessary films in the MCU. 569