I've split a party intentiionally several times in ooooo...30-odd years of gaming. It can be done, and work very well, if handled carefully.
One Call of Cthulhu game I forcibly split the party by having a Tentacled Horror errupt out of an alleyway just as the party passed by. The party was split down the middle. I put half the players in one room and the other half in another. I ran between the two. One team stayed to fight while the other guys continued to the Ancient Bookstore to research what they were fighting against. It worked well, with 3 guys steadily losing HP (and ammo!) while the other team raced against time to find what they needed and return. It put real pressure on both sides, especially as I wouldn't let them communicate at all

The bookstore guys half expected to return to the sight of mutilated corpses!
Heck, splitting the party is a part of the fun in horror gaming. Put a cellar in any building and there's bound to be one player who wants to go down there on his own. It's the Done Thing.
In a HERO superhero game splitting the party isn't the problem if they have some form of instant communication. That way they're not really split, even though they might be physically separated. I've gamed sessions where one player was the HomeBase tactical computer; he never went on adventures per se, but co-ordinated the attacks using long range radar, etc. Work well until he went insane and took over the base......but that's another story.
Same for D&D really (apart from the insane computer taking over the base bit). As long as the characters can communicate remotely, there's no problem. I ran the Githyanki Invasion where the players were a strike force that cut supply lines, fireballed weapon stores, etc. Kinda Twilight-2000 meets the Lich Queen. They all had Bonded Rings that telepathically linked them together, making for very effective strike tactics. The rings were a gift from some Githzerai. I recommend them for any party of adventurers above 6th level as it gives the party a much greater effective range; they don't all need to be within shouting distance of each other during combat.
So yes, spltting the party /is/ possible, but it takes some forward planning to run effectively.