This has nothing to do with Starcraft the game and everything to do with Starcraft the universe.
I like Starcraft! Both the game and the universe. The game is a robust real-time strategy classic, the universe one of the more enjoyable in video games, managing a science-fiction setting with a dash of humour. But that universe is - like most fictional worlds - not entirely of its own making. Just like Star Wars is The Hidden Fortress with lasers, Starcraft owes a creative debt to Games Workshop's Warhammer 40K.
All three of Starcraft's races are based largely on factions from the Warhammer 40K series of tabletop miniature games, which pre-dates Starcraft by over a decade. Long time and/or hardcore Starcraft fans will probably already know this (Judging from the number of Horus jokes in the comments of a previous post, 40K fans do too), and for you, there's not much more to read here if you're the type to get angry at people pointing this out.
If you're simply a casual fan of Starcraft, however, and like the whole Marines + swarming alien menace + wise old alien race thing it has going on, then use this as a launching point to learning more about the franchise's creative predecessor!
Below are the key areas - the factions - in which Starcraft is heavily based on Warhammer 40K.
SPACE MARINES - The most immediate and obvious comparison between the two. Starcraft's Marine and 40K's Space Marine are both the backbone of their respective armed forces, both have the word "marine" in their name and, most critically, both look eerily similar. Big collars, big boots, big shoulder pads.
What's not the same? Starcraft's humanity is a dishevelled, splintered group that's a little rough around the edges. Truckers in space, as they were originally portrayed. 40K's are a vast empire with an ancient mythology, and are about as far removed from truckers as you can imagine.
PROTOSS - The Protoss are the most advanced race in the Starcraft universe. There are "light" Protoss and "dark" Protoss. They are a proud and ancient people. They possess psionic powers. Everything I just said also applies to the Eldar, the elves of 40K's universe, whose elegant and ornate armour even looks a little like that of the Protoss.
ZERG - Starcraft's third race is the Zerg, a swarming race of insect-like creatures operating as a devastating hive mind. The Tyranids, a major faction from the Warhammer 40K universe, are a swarming race of insect-like creatures operating as a devastating hive mind.
So, yeah, while the storylines and adventures of the two universes are radically different, on a fundamental level, Starcraft is built on the same foundations as Warhammer 40K. Just without the Orks. Or Chaos (though you could argue there's a little of that in Starcraft's Kerrigan). So if you're a fan of Blizzard's series but have never really looked into 40K before, maybe now's the time to try! It's not like Blizzard looked to it for inspiration because it sucked.
If you want to read up on the history of the universe and the tabletop game based on Warhammer 40K, this wiki page is as good a place to start as any. And if you want to play some Warhammer games? May I recommend Dawn of War and Dawn of War II on the PC, or if you're after something a little more retro, Space Hulk, again for the PC.