Tricky one. My number one recommendation is unfortunately out of print, so I’m going to provide a couple of backup options as well.
My top marks to go Marvel Heroic Roleplaying. One of the final titles from Margaret Weiss Productions before she left the tabletop RPG biz to focus on her film projects, it’s a fascinating bit of genre emulation that “gets” Western superhero comics like no other game I’ve ever seen.
Mechanically, the core of the system is Affiliations, which take the place of more conventional traits like Strength or Agility. The three Affiliations are Solo, Buddy and Team, with their ratings reflecting how effective each hero is in various contexts. For example, if your highest rating is in Solo, you can basically use your best stat whenever you want, but you can’t roll Solo and accept help - mechanically represented by lending dice - at the same time, so the price you pay for self-sufficiency is vulnerability to being ganged up on. Conversely, if your highest rating is in Team, you’re basically unstoppable with your squad at your back, since you can stack your best Affiliation on top of all those assistance dice - but if you’re caught alone, you’re doubly hosed, since you’re denied access to your best stat on top of nobody having your back.
This is paired with super-power mechanics that rank various abilities in terms of productivity, not just in terms of scale. There are only three “grades” of superhuman traits, with significant overlap, so it’s entirely possible for, say, Captain America’s Super-Strength d8 to beat the Incredible Hulk’s Super-Strength d12. This doesn’t mean that Captain America overpowered the Hulk; it just means that Captain America’s super-strength ended up helping him in that situation and the Hulk’s didn’t. Figuring out what that means in narrative terms is up to the players.
Beyond the basic dice-rolling mechanics, MHR is notable for breaking the “one player, one character” convention harder than just about any other game I’ve ever seen. You can bring your own original character to the table if you want, but each scenario also comes with a roster of pre-statted heroes who are participating in that event, and anyone can jump into any role at any time. Yes, any time. Not only does this mean that you won’t necessarily be playing the same hero in every scene, it means that a given hero won’t necessarily be played by the same player in every scene!
It’s both accepted and expected for players to call dibs on their favourite heroes - so, for example, you can say that you get to be Spider-Man in any scene where he’s present - but if nobody calls dibs on a given role, that character can end up getting passed around a fair bit. I once participated in session of MHR where the Hulk was played by a different player every single time he showed up, and great fun was had by all.
Like I said, it’s out of print (the publisher lost the license from Marvel back in 2013), so buying used is your only option here. That’s why I’m going to provide a backup recommendation:
This isn’t a standalone game; rather, it’s an add-on for the fantasy roleplaying title Savage Worlds. I’ve recommended other games that build on Savage Worlds in the past, some of them superhero-oriented themselves - like The Kerberos Club, if Victorian urban fantasy superheroes are your thing. The Super Powers Companion is a non-milieu-specific adaptation of the same material, so it’s good for pretty much whatever you want to do with your supers. The buy-in’s a little pricey, since you’ll need the Savage Worlds core rulebook to use the Super Powers Companion, but that’s not necessarily a bad thing if you’re looking to start a collection, since there are any number of other games that also build on the Savage Worlds core.
No real surprises here - this is a much more conventional game than Marvel Heroic Roleplaying. It stands out from the crowd mostly in terms of accessibility. If you want something goofy and esoteric, that’s where my second backup recommendation comes in:
This one’s a localised Japanese RPG about people who’ve been infected by an alien virus that gives them super powers. Uncommonly for superhero RPGs, it’s basically a class-based system, with each “character class” representing a particular syndrome caused by the virus, ranging from the gravity-manipulating Balors, to the shapeshifting Exiles, to the hyper-intelligent Neumanns.
Like many Japanese tabletop RPGs, Double Cross incentivises engaging with the interpersonal side of play by literally blowing up your character if you don’t. Cultivating relationships with regular humans - amusingly termed “Loises” by the system - is the only way to prevent the super-virus from turning you into a monster, so there’s a constant cycle of powering up to beat the baddies, then cooling off via low-key interpersonal scenes. Or, you know, just going all out and blowing yourself up.
Now, I want to caution that this isn’t the best translation. Some of the localised Japanese titles I’ve recommended in the past, like Ryuutama or Golden Sky Stories, have had very good English localisatons. This is not the case with Double Cross; its English ranges from stilted to downright gnomic, though the latter is thankfully rare. It’s totally playable, but not always the easiest read.
Double Cross is definitely more on the Prototype/Infamous end of the superhero scale than the Avengers end (with perhaps a sprinkling of Persona if you stick with the game’s default high school setting), so it may not be what you’re after - but if it is, you can grab the core rulebook in PDF here. The printed version is out of stock with the publisher at the time of this writing, with no ETA on a reprint.
Tabletop recommendations: Urban Fantasy with at least one non-humanoid playable race, fusions of magic and technology and little to no Masquerade. Also, a superhero RPG themed mostly after the Silver Age and a Steampunk RPG that lacks, or, better yet, explicitly acknowledges the weird Pro-Imperialism subtext lots of Steampunk has.
Would you believe that there’s a single game that satisfies all of those criteria at once?
Yes, this is, in fact, a class-conscious Victorian steampunk supernatural urban fantasy superhero game*, and while its superheroics do tend to be a little Bronze Age by default, it can totally do Silver Age with only minor tweaks. It’s been republished for three different systems - Wild Talents, Savage Worlds and FATE - so you can pretty much pick your poison in terms of game mechanics; I’ve linked all three versions above. Note that the Savage Worlds edition is not standalone (i.e., it requires the Savage Worlds core rulebook to play), so if you’re looking for an all-in-one package, it may be best to go with one of the other two. You should be able to find descriptions of what each system plays like fairly easily via Google.
* I wasn’t kidding when I said there’s a game for very nearly any desired experience of play. It’s a diverse hobby!