(Note: I'm talking about movies here, since in the comics, he has, though I think he's on probation or something like that because of stuff done during the whole "Superior Spider-Man" thing, which I might later talk about)
The Amazing Spider-Man 2 did not do too well, and recieved mixed reviews. I personally thought it was alright, better then the previous movie, but perhaps it's from lowered expectations, since it did have problems (Unneccesary Rhino, repeating the "way too many villains" problem from Spider-Man 3, and having little development of many characters to name a few). Anyway, due to the box-office inadequacy, Sony's plans for everyone's favorite web-slinger are kind of up in the air. From what I've heard, the Venom movie, which was in development before the first Spider-Man movie came out, has been scrapped; The Amazing Spider-Man 3's release date has been pushed back; and the Sinister Six movie (which was hinted at with about as much subtlety as the cameos in the pilot episode of Gotham) is supposedly a "soft reboot". Why? Well, the previously stated box office disappointment of ASM2, and the fact that, according to Screenrant, "...Sony executives are toying with the possibility of using future installments to establish connections between Disney's ultra-popular Marvel Cinematic Universe..." In other words, if negotiations go through, Spider-Man might join the Avengers on the big screen!
Now, a bit of background: The rights to certain Marvel characters are divided between a few studios. Fox owns X-Men and the Fantastic Four; Sony owns Spider-Man; and Disney owns the Avengers and Guardians of the Galaxy (among others). That's part of why there are more Marvel movies coming out than DC movies: the rights to the DC characters are owned by Warner Brothers.
Anyway, would it be a good idea for Spidey to go with the Avengers? Yep. Honestly, I kind of hope Disney acquires the rights from Sony, and add the webhead to the MCU. That way, he's part of that continuity, and the burden of creating a "shared universe" won't fall squarely on Spidey, which is what Sony is trying to do, along with Fox and DC for their respective properties. It might work for Fox because they have X-Men and Fantastic Four, so they could have multiple team-ups/crossovers, and, if done right, it could work for DC (I, based on what I've heard, think the implementation of the DC shared universe will suck, but that's a rant for another time). But it's a problem for Spidey, because he's one character. Granted, Sony is trying to do spin-offs, but that's quite a burden to place on one character. It worked for Disney because there were multiple characters.
So, yeah, Spider-Man should join the Avengers, so that way his movies won't suffer from "Iron Man 2 Syndrome" (where a movie is trying really hard to build a shared universe, and over-stuffs it, creating a less-than-good movie just to establish certain things), and instead focus more on the character of Peter Parker/Spider-Man, because that's pretty much what Spider-Man is and should be: character focused. Also, I'll admit, it would be kind of awesome to see Spidey trading smartass comments with Tony Stark.
Oh, it should be noted that the whole "Spider-Man joining the MCU" thing is a rumor, and might not happen, but hey, you never know. Until then, I suppose we should just wait, and be glad that, of the mistakes that both Spider-Man 3 and The Amazing Spider-Man 2 made, one they don't have in common is the Spider-Strut.