A problem I have with a lot of published settings and home brew settings (mine included) is that all the cool stuff has happened to other people. There doesn't seem to be anything for the PCs to do that's big or important. As creators, we're so interested in filling in the blanks that we fill in every bit of space, like the artist in Tim Powers' Drawing of the Dark.
When some awesomely awful threat comes up, you don't want the players to say, "Hey, let the analogue of the Avengers or the JLA handle it."
One way that you can handle it is scope: yeah, the Avengers protect the world, but the players have Hell's Kitchen! That's fine if that's what the players want, but if you occasionally want to throw in some world-destroying monster, you have to expect the PCs to hand off the ball. "Hey, this Cthulhoid thing just showed up, and I've got you on speed dial for just such an emergency. How soon can you get here?" And, in fact, you can spin a whole evening out of the holding action while they're waiting for the experts to arrive. ("Nobody said it could duplicate itself! Why didn't Professor Wyrd send along notes?") If you're usually happy playing at that level, that's great.
Another kind of scope is concentrating on only one particular kind of threat; I ran a campaign where the heroes were all involved in the mystical side, and someone else in the group ran the campaign where the heroes were "regular" heroes. (I believe we even had a crossover.)
Another way to handle it is by having the PCs be the first or greatest superheroes. They get the threats no one else can handle because they are the Justice League or Avengers analogue. You can have heroes who are the greatest or you can have them simply be the first heroes that ever appeared.
Closely related to that are that the PCs are legacy heroes who have been called to step up and replace the big guns.
It's possible that you could go the route that both Base Raiders and Necessary Evil have gone, and all the heroes disappeared before the campaign started. (Base Raiders made the villains disappear, too.) The PCs can't call anyone in, because they are all that's left.
The intermediate is that the PCs are the B-team. They handle their own stuff, but when the heavy hitters are off-planet or are incapacitated, the PCs get called in. It's a nice way to spend most of your games on city- or country-wide threats, but occasionally throw in some cosmic ones.
Another way to occasionally throw in something big is the secret history. For whatever reason, they can never tell anyone, so they have to handle it themselves.
On a meta level, don't create so damn much history when world-building. Those neat things, let the players encounter them. Make sure that the NPC heroes are no longer useful or are busy.