As others have said, progressing to a certain point in the main questline will earn you the title of Thane, and a Housecarl by the name of Lydia.
You can also hire mercenaries at various inns across Skyrim. Jenassa, for example, is available for hire in the Drunken Huntsman, the hybrid inn/hunting supplies shop near Whiterun's main gate. You'll also be able to take certain people on as followers after doing favours for them or beating them in brawls. For example, helping either Faendal or Sven with their love interest in Riverwood will allow you to take one of them as a follower. L
Followers will stay with you for as long as you like. Most, however, have a level cap of 50, meaning they'll stop levelling once you hit that level.
They will protect you and they can't die. Unless you kill them
Untrue. I've seen Lydia killed by a frost troll, and I didn't hit her.