In the order the top ones go from left to right I believe it goes: 60's Spider-Man, 70's Spider-Man, '94 Spider-Man, and '99 Spider-Man Unlimited.
Then below it's a little out of order. I believe the one in the bottom is the 2003 Spider-Man from The New Animated Series, then we have Ultimate Spider-Man from both Avengers: Earth's Mightiest Heroes (Darker blue and red suit on the left who showed up in season 2 I believe) and the Ultimate Spider-Man cartoon (Lighter red and blue on the right of the 2003 Spider-Man).
Then of course we have Spectacular Spider-Man which was from 2008.
It just had slightly updated animation is all. We get some of the Spider-Memes from the 70's show.
I grew up on the '94 Spider-Man, it holds a special place in my heart.
Spider-Man Unlimited ('99) was a FANTASTIC show where Spider-Man goes off to this alternate Earth to save John Jameson!
2003 Spider-Man The New Animated Series was alright. The animation really needed a lot of work but some of the stories were intriguing. It's also the one where Neil Patrick Harris voiced Spider-Man!
Nono, not in an Avengers movie, but in an Avengers cartoon. Avengers: Earth's Mightiest Heroes was the cartoon that they had going before they cancelled it and brought out Avengers Assemble. Ultimate Spidey showed up in Earth's Mightiest Heroes and since that tied those two universes together, Avengers Assemble is actually a sequel to Earth's Mightiest Heroes, even though it's kinda mediocre. The episodes Spider-Man shows up in for Earth's Mightiest Heroes are actually a lot better than most of his episodes in the Ultimate Spider-Man series imo.
Ultimate Spider-Man is fun to watch, there isn't much of a story till you get to the Goblin episodes and Season 2 has the better stories by far imo.
I LOVED Spectacular Spider-Man!! Josh Keaton voiced him and the stories, how it all fit together was perfect! It also had the wisecracking that some of the other series didn't nail quite right. The villains and the characters in general were all pretty well rounded, including Electro. The Goblin arc in the series was so well done and they had Steve Blum voice the Green Goblin! All in all it ranks the top of my list of favorite Spidey cartoons.