The galactic map is large, and difficult to navigate quickly. Just looking for a summary of how many worlds I'd be hitting if I decided to see it all - are we talking dozens? Hundreds?
Well, the good news is that the number of explorable planets is a much smaller subset than the number of total planets in game. You can see the list of every planet and scannable object here , but note that for a good 60% of those planets, there is text only -- no mission, possibly some resources or collectibles, and a description of the planet's characteristics.
More relevantly, there are a total of 39 systems, each of which generally has one mission on it, with the hub planets, of the Citadel, Noveria, and Feros having more than one (though they take place in the same relative area).
So all in all, there may be a lot of worlds, and space may be big (really big), but "exploring it all" is something that is wholly manageable, and easily achieved by those willing to dedicate the time to it.