The key ones I'd like to see are:
1. Spider-Man and Falcon. They teamed up at least 3 times in Marvel Team Up. They could both fight the Vulture, and feature an aerial chase and dog fight between Falcon and Vulture. Since Anthony Mackie might not have as large a role in Civil War, this would be a good way to have him feature a bit more.
2. Spider-Man and Ant-Man. Ant-Man doesn't seem to have any sequels planned after next year's movie. This would be a good way to have a quasi-sequel while having a Spider-Man film at the same time. They could fight one of Hank Pym or Scott Lang's villains or a combination of Ant-Man/ Spider-Man foes.
They could fight Taskmaster, who should be introduced into the MCU. That would allow Ant-Man to have his sequel but also allow Spider-Man to get a film as well, killing two birds with one stone.
3. Spider-Man and Daredevil.
This seems like a natural one. They could take on the Kingpin and other mob-related villains who would usually feature in a team up: maybe Tombstone or Hammerhead. They have actually both fought the Blizzard together before. Beetle is also a common foe.
Spidey and DD could even potentially fight Electro:
Although they might want to stay away from that after ASM2.
4. Spider-Man and Punisher. Typical team up from the comics. Would be a chance to introduce the Punisher again into the MCU without him needing to be one of the team up heroes as such. He could even be the catalyst who brings Spidey and DD together.
Maybe Spidey alone could save the Kingpin from the Punisher, unaware at the time of who Wilson Fisk is. He would just be doing his heroic duty and trying to save all people, but that could initially bring him into conflict with DD, who will already have dealt with Fisk in the Netflix series. Eventually Spidey and DD could team up and take down Kingpin a) because DD needs someone else to do it and b) so that they can prevent the Punisher from taking the law into his own hands and giving street heroes a bad name (and potentially starting another civil war).
5. Spider-Man and the Netflix Defenders. These are natural team ups as well. Imagine Spidey with DD, Luke Cage, Iron Fist and Jessica Jones. This would give them a chance to bring them all to the big screen.
6. Spider-Man and Ghost Rider. These two teamed up in the comics. Don't know who they could fight, but would also provide a chance to bring back Ghost Rider to the big screen while not having to lead his own movie.
7. Spider-Man and Iron Man. This would be a huge team up movie of both of Marvel's top two heroes. Imagine the box office potential. There are numerous villains they can fight. Beetle again is a common foe. They also both fought Radioactive Man together.
8. Spider-Man and Captain America. Another potential box office smash. These two are a classic pairing with any number of foes to face together.
Of course, while there is box office potential for Spidey with Cap or Iron Man, it's probably better to showcase a lesser hero who won't get the spotlight.
9.Spidey and Tigra vs Kraven
10. Spider-Man, Silver Sable and Sandman vs the Sinister Syndicate
Don't know about Rhino, but if they do use him he would be done properly as an actual person instead of a guy in a big mechanical suit. Hydro Man would look great on film. Boomerang might look similar to Captain Boomerang from either Arrow or the Suicide Squad, but they made him look badass in Arrow.
11. Spider-Man and Captain Marvel/ Ms Marvel
That could be a good way to popularise her and have her feature in another movie other than her own.
12. Spider-Man and Black Panther