In Marvel Cinematic Universe, I know of only one human who has visited Asgard: Jane. What about comics? Is visiting Asgard more frequent in the comics? Have Avengers visited it?
Yes, the Avengers have been to Asgard as recently as the "Fear Itself" saga in 2011. They have been there multiple times in their history, usually because of a threat from Asgard such as Loki or the Destroyer or Karnilla, or Loki, or the Enchantress, or Loki or Hela. Mostly Loki.
In the previous year's Siege storyline, the leader of HAMMER, Norman Osborne lead an assault on Asgard with his evil Avengers. He was in league with, you guessed it, Loki.
The New Mutants have also been there in issues #79 thru 85, I believe.