Ever since Marvel Studios successfully proved that a shared cinematic universe can work, with comic book characters showing up in other character movies and eventually teaming up in The Avengers to fight off a greater threat - and win at the box office - a new precedent has been set. And fans want more.
If Captain America, Hulk, Iron Man and Thor can team up, why can't they team up with other popular characters from Marvel Comics in Spider-Man and the X-Men? The simple answer is because different film studios hold the film licenses for these different franchises, but that doesn't mean it cannot or will not happen. In fact, there were talks of the beginning of such a thing happening between Marvel Studios.
In chatting with Reviewer.fr, Marvel Studios President of Production Kevin Feige confirmed that Marvel spoke with Sony about the possibility of including the Oscorp tower from The Amazing Spider-Man in The Avengers but the deal was never really close to happening. That conversation though means they're willing to talk and it also means that the seemingly separate Marvel universes that each studio is attempting to build can connect, eventually.
Questions about a crossover, with franchise characters making a cameo appearance in another studio's film, are consistently brought up by the talent and execs at Marvel, Fox and Sony before. And the topic will not die until it happens and eventually it could, but not for a long time. Each of the studios have enough work ahead telling their current stories or (re)establishing key properties so it's simply too early for large crossovers to occur. Especially for Marvel's young studio which is still just laying the groundwork and introducing new characters for years and years to come.
"I would say not anytime soon. Would we be in a position to team up with other studios who have a few of our characters - because we have so many of our characters ourselves - but I would never say never."
If Marvel was in a rush for a crossover, to include Hugh Jackman's Wolverine (he's absolutely interested) or Andrew Garfield's Spider-Man (who also wants to join The Avengers), then they missed out on a major opportunity in the Quicksilver situation, where directors Bryan Singer and Joss Whedon both cast their own versions of the character for X-Men: Days of Future Past and The Avengers: Age of Ultron, respectively. Quicksilver could have been the perfect shared character to bridge the universes together but he's instead being used very differently in each movie, even in different time periods.
But rushing they are not. Feige previously went on record explaining that he and the decision-makers at Marvel have movies tentatively planned until 2021 with their own characters and there's really no room for a full-on crossover "event" film like we see in the crossover events in Marvel Comics. Even if a deal was struck by the studios to share characters, it wouldn't start with a full blown crossover.