Here are my picks for the top five most iconic covers featuring Hawkeye (with iconic being determined by what covers are most established and most recognized when it comes to Hawkeye, with a preference towards covers that are homaged a lot). This is not a BEST cover list and due to the very nature of icons, very few (if any) recent covers will be on the list. A notable exception to the rules is that I don't count covers from a character's first appearance (which isn't applicable to all characters, of course, just those who appeared on the cover of the comic they debuted in), as those tend to be automatically iconic so they're boring. Here's a list of all characters featured so far.
First off, while I'm exempting first appearance covers from the countdown, it's only fair, I suppose, to share them here before the countdown begins, so here is the first cover appearance of Hawkeye from his debut story, Tales of Suspense #57...
Artist: Don Heck
Artist: John Byrne
Possibly the most iconic Hawkeye story, this is the one where he fights Deathbird. Almost a perfect encapsulation of the character. This is a very strong cover from Byrne.
Artist: Bob Hall
Amazingly enough, this is one of the most homaged Hawkeye covers (by which I mean, of course, that it's been homaged at all).
The West Coast Avengers are a big part of Hawkeye's history (as is Mockingbird, who's on this cover).
Artist: Ed Hannigan
This cover would be higher but, well, it's Hawkeye and Ant-Man II.
Artist: Sal Buscema
Not much to say about this one except that it's a classic Hawkeye cover (surprisingly, Hawkeye really did not get that many cover spotlights in his early days as an Avenger - the one exception was when he was not even Hawkeye, but Goliath!)
Artist: George Perez
Again, not much to say except that it's a classic Hawkeye cover.
LAST COVERS CUT: The aforementioned Goliath cover was excised when I decided to do just Hawkeye cover rather than Clint Barton covers, and the cover of Hawkeye's mini-series certainly has some historical significance, but I think the West Coast Avengers cover takes care of most of that, and Gruenwald's Hawkeye #1 cover really isn't all that great of a cover. Al Milgrom's West Coast Avengers Hawkeye cover for Marvel's 25th Anniversary is a strong contender, I suppose. There's a cool Marvel Team-Up cover with Hawkeye and a decent Defenders cover.