...so let's take a look back at those team ups, and let you decide how much you liked them....
Hawkeye had just left the Defenders (who he briefly worked for during the Avengers/Defenders War, having just left the Avengers before that), and called on Spidey for some help with a problem he had encountered, and following the thieves back to their HQ led the heroes to a confrontation with Fantastic Four/Silver Surfer foe, Quasimodo! With a little of Hawkeye's archery daring-do, the heroes were able to stop the villain and go back to their normal lives.
New Hero, Old Villain
Spider-Man thought he was attacked by the Human Torch and Iceman while swinging through the city (and was saved from drowning by Hank Pym, known then as Yellowjacket). Hank took Spider-Man back to his apartment (with his wife, Janet Van Dyne, aka the Wasp, who was none to happy to have their romantic night ruined), but soon recounting the details, Spidey realizes it was the villain Equinox (whom the Torch and Iceman fought in an earlier issue of MTU), and the three heroes went in search of the villain, with potentially catastrophic results for Hank Pym to end the issue...
New Villain, Old Name
This story starts out with Hawkeye attacking Spidey, not wanting to let Spidey hurt him. After soon dealing with an unconscious, overworked Hawkeye, Spidey talks to the former Avenger, who was now working for Cross Technological Enterprises as security chief, he encountered thieves, including the new Mr. Fear, who dosed Hawkeye with his fear gas. The two heroes face their fears and Mr. Fear, eventually defeating the villain after they realize that there are emotions more powerful than fear....
New Villain, Hero With Old Namenew Ant-Man, Scott Lang, showed up to meet Spider-Man in Marvel Team Up #103 (March, 1981) where the two heroes faced off against the villain with the photographic reflexes, the Taskmaster, and his business, "The Assassin Academy!" by writer David Michelinie, penciller Jerry Bingham and inker Mike Esposito.
This time around, Ant-Man was busy fixing his daughter's ROM doll (but had to do it under cover, as Cassie didn't know her dad was Ant-Man), when he has an old friend of is approach him to help him find work (as someone recruits ex-cons to pull jobs, and pays for success or failure). Since Scott gave up that life, he declines, but gets involved when he reads in the Daily Bugle his friend had died the night after approaching him. Peter Parker is also snooping around, looking for photos to sell to J. Jonah Jameson...and the two heroes encounter the Taskmaster, and his newest scheme to train the criminal element. Spidey and Ant-Man do defeat Taskmaster (who uses skills learned from watching Daredevil and Hawkeye against the two heroes), mostly by Ant-Man using his own powers in an unexpected way (that of enlarging an ant to attack), but while the heroes stopped the villain's plans, Taskmaster got away.
Hawkeye, it was almost like having Spidey, Ant-Man and Hawkeye in an issue, and there are more related Spider-Man and Avenger member team-ups to come!