If you know anything about Deadpool, he has a way of making uncomfortable situations infinitely more uncomfortable. One of the things that makes this unlikely bromance so great is the constant...friction.
Eventually, Spider-Man was worn down by Deadpool's friendship advances and now humors him. Sure, he's confused by his constant fourth wall breaking, but he seems to enjoy his company now...well, a little more than he used to.
Though they're buddies, Spider-Man's Spider Sense is still set off by Deadpool. Can't blame it. Hard not to feel in danger constantly around a mentally unstable mercenary with loads of guns, explosives and sharp pointies.
This is truly a magical bromance, as Spider-Man tries to fix the broken Deadpool. Usually in relationships this means making him dress more properly. In this case, it involves attempts at curtailing an incessant love for murder and mayhem.
Deadpool has learned he can rely on Spidey when he's in need. Whether just to have someone to go to the movies with or save him from Hit-Monkey (yes, this character is exactly what it sounds like), he's got a friend in Peter Park...
Ultimately, Spider-Man and Deadpool get along because of their similar senses of humor. Spider-Man is known for making cute, punny quips in the heat of battle, while Deadpool never shuts up about boobs and Bea Arthur. Close enough.