In Minecraft, is there a way you can spawn a creeper without the egg?

According to the Minecraft Wiki:

The creeper was accidentally created by Notch, the creator of Minecraft. While Notch was trying to create the first-ever passive mob, the pig, a coding mistake was made, and he accidentally swapped the height and lengths of the pig's build.

Instead of just discarding the bugged creation, he decided to reskin and program the glitched pig to explode, thus creating the creeper.

And, to answer your second question, you can very easily summon a creeper, by simply using the command: /summon creeper ~ ~ ~