When Captain America: The Winter Soldier came out a bunch of unimaginative nitpickers were all like, "Wait, where's Hawkeye while all this SHIELD stuff is going down?" I basically No-Prized it for them here, but it turns out that Hawkeye was involved in an early draft of the script. On the Winter Soldier blu commentary we learn that Hawkeye was tasked with hunting Cap down after he escaped the Triskelion, which actually would have been cool. There's a deleted scene where Cap abandons his SHIELD agent outfit because it has a tracking device and Hawkeye would have been the guy leading the Strike team that followed that tracking device.
But just because ol' Hawk hasn't been in a Cap movie yet doesn't mean he won't ever be in one. Talking to Collider Jeremy Renner had this to say about his post-Avengers: Age of Ultron MCU career:
“There are rumblings of Captain America 3. I don’t know what’s going to happen there. I’ve got to find the time, man (laughs). I’m trying to stay home and I can’t.”
Captain America 3 would be a continuation of The Winter Soldier, with Cap continuing the hunt for Bucky. Having Hawkeye appear would make sense, but hopefully not at the expense of Black Widow. The chemistry between Steve and Natasha (and Chris Evans and Scarlett Johansson) is spectacular, and their friendship was one of the best parts of the last film.
I'll be kind of honest: I'm not a huge fan of the MCU Hawkeye. He just hasn't popped. I know he has more to do in Age of Ultron, so here's hoping that Renner wins me over this time.