It has often been remarked that high-level D&D campaigns often approach superhero campaigns in power level and scope - the PCs can mow down lesser mooks in large numbers, and the threats they face are often world-shattering, and essentially unstoppable by less experienced characters.
So... why not run such campaigns as superhero campaigns in the first place? The Forgotten Realms, in particular, seem well suited for such a campaign, as it is positively awash with high-level characters and threats.
There would have to be some changes in gameplay, of course. First of all, the usual profit motive - "kill monsters and take their stuff" - would have to be deemphasized. The PCs aren't roving murderhobos, they are heroes and protectors! If you use some iteration of D&D, it makes sense to just give the PCs some "level-appropriate" funds to get magic items and gear, while assuming that any stuff they find during actual play (apart from unique artifacts) is spent on research/home base/lifestyle/parties and so on. That will hopefully help the players to get into the proper frame of mind. If you are using a different system, assume the PCs can get "mundane" gear and pay for especially fancy stuff or prominent magic items with character points (or whatever the system uses).
Then you have to give some thought to the character's "home base". While there are "roving superheroes" who travel the world, most of them tend to stay close to a particular region. What would Batman be without Gotham City? For the Forgotten Realms, you can either pick a particular region (the Silver Marches, the Moonsea, and so forth), or a particular city - and there is no shortage of cities in the Realms with detailed city plans (although few can approach Waterdeep, which holds the same spot as New York City in the Marvel universe). And just like superheroes, heroic adventurers will often have rather ambivalent relationships with the local authorities. They may well be feted when they thwart the latest threat to the region, but the authorities are also too aware that the heroes aren't really under their control, and that they would have difficulties stopping them, should the need arise...
Secret identities probably won't translate very well, since adventurers are generally assumed to be famous - though the odd "mysterious masked wizard" is certainly appropriate. Do encourage the players to come up with interesting nicknames, as well as a good name for their group as a whole (which also is tradition in the Forgotten Realms).
Then it's only a matter of having Bad Guys show up in their territory and be up to no good - and here is where the richness of the Forgotten Realms setting really shines. The Red Wizards of Thay! The Zhentarim! The Dragon Cult and the Kraken Society! The Empire of Shade! Add to that various powerful monsters, both organized and unorganized, and you will be able to copy most comics plots with ease. Even tales of Science Gone Wrong can simply be converted into Magic Gone Wrong.
And it is easy to increase the power level further, leading to continent- or even world-spanning team ups, with the heroes standing side by side with NPCs like Elminster and the Simbul, creating their own equivalent of the Justice League and the Avengers to deal with world-shaking threats...