I prefer Hawkeye's classic costume, but I did try to update it a little. I like that his more modern costume uses a chevron to represent movement and the arrowhead, but his modern costume is a little too black and "practical" for me. I went with a sleeveless version of his traditional costume but used the chevron where his (admittedly ridiculous) mask attaches to the rest of his costume.
Black Widow has had a pretty consistent costume over the years with minor changes here or there. The thing that seems to change most is her hairstyle. Even in the movies she changes it every time we see her. I went with longer hair and I like to draw it draping over one eye. I think it helps give her a bit more of a mysterious look.
Hulk doesn't have a ton of costume options, but I do like the idea of him getting more of a uniform instead of just pants that he rips through each time he transforms. I like the idea of Hulk having some control over himself for the greater good of the team.
Thor is one of my favorite Avengers and I have a lot of fun drawing him. I try to make him even bigger than the typical guys like Cap so he seems even more godlike. I've finally switched over to the full metal helmet instead of the feathery wings. It allows me to keep him more streamlined and angular and I don't have to try to figure out where the wings attach to the metal. Some of his costume elements were actually inspired by his look for Disney Infinity.
Iron Man is a great character, but not one I like to draw very often. I've never been comfortable drawing more mechanical characters like him, even with my more geometric style. I do really like the way this drawing came out, though. I took inspiration from a lot of his more recent armors, including ones from the movies.
For my Captain America design, I pull a lot from Earth's Mightiest Heroes -- with the black shadowing around his face leaving gaps to indicate his eyebrows. I also try to incorporate a little of his more modern costume elements including the gray side panels and stars on his shoulders. I prefer the more traditional mask over the helmet with chinstrap though.