The Avengers are made up of superheroes who are so powerful that it's got to be tough to come up with a menace big enough for them to bother with every month. Therefore, the Avengers covers generally feature some enormous threat to the very fabric of the universe!!!
Either that or someone's brother or evil, robot "child" shows up and annoys everyone by trying to kill a lot of people. Seriously, these guys create their own problems.
Anyway, the covers below are my favorites.
This is one of the first Avengers covers that made a big impression on me. I was all, "Wha-HUH? Who's that dude and why is he dressed like all the Avengers at the same time?". That dude is Taskmaster and he is one of the biggest badasses in the Marvel Universe. He has "photographic reflexes" which means he can perform any physical activity which he can observe. Therefore, he is able to mimic anyone with "normal guy" powers such as Hawkeye or Captain America. He can also watch any hero and figure out the best way to defeat him or her. That pushed all the right buttons for me at the time and I still think he's a great concept.
This is the first comic I remember reading which dealt with a "serious real-world issue", in this case, domestic abuse. Yellowjacket wasn't on trial for hitting his wife but that action was the last straw that got him kicked out of the Avengers. The issue depicted Henry Pym's breakdown well. There are those who believe that Jim Shooter destroyed the character for future writers with this story but I disagree. Pym's attempts to rebuild his life made for some great storytelling.
I like the snow effect on this one but the main reason it's on here is that it is one of the best of the covers depticting something so powerful that it doesn't even notice the Avengers. This is the kind of opponent the team was often up agaist. Their real challenge was to find a way to get around the invincibility of the Big Dude of the Month.
This is my absolute favorite Avengers cover. It has a permanent place in my ever-shifting Top Ten Covers Of All Time list. I mean, look at it! That is 100% certified badass!