The lights are on
Among the many things to do in Skyrim, you have the ability to gain someone's trust and have their steel or magic skills complement your own, by fighting alongside you. They are a fighting force, item repository, and friend. I, having had many of these followers as my own, decided to make a list of the best followers to choose from, depending on your playstyle.
Cicero/Dark Brotherhood Initiate
Cicero is only available at the end of the Dark Brotherhood questline, and, SPOLIER ALERT!, can only be recruited if you leave him alive. Personally, he is my favorite, because he's certifiably insane, and he spouts some pretty funny jests...(pardon the pun.) Also, you can get the Dark Brotherhood Initiate as well, and they have the same stats as Cicero, but are not nearly as funny. He complements sneaky characters well, and can hold his own in an all-out fight, especially if you give him some good gear to wear. Cicero's major skills are: sneak, light armor, one handed, and archery.
Mjoll The Lioness
While there are many different "tank" followers in Skyrim, one stands a cut above the rest: Mjoll the Lioness. Why? Because she's invincible. See, after her quest to gain her as a follower, she is still marked as "essential", meaning she won't die, no matter how many fireballs you sling at her. To start her quest, you have to go to Riften and talk with her, be level 14-15, and you must delve deep into a dwarven ruin. Her invincibility is great for mage characters, because you can rain down magic without fear of killing her. She can also be married, if you're "into her." xD Mjoll's major skills are: heavy armor (100), two-handed (100), block, and archery.
J'zargo is a College of Winterhold apprentice, yet has superior Destruction magic skills. He also will level his skills up as you level up all the way. He is a bit cocky, but once you get over that, he's an excellent companion and will save your life several times over. The quest to gain him as a follower is relatively easy; all you have to do is try a few spells out for him. This is a solid choice for a warrior who's having some trouble. He's also good at complementing an archer's skill-keeping the hordes at bay while you fire arrows into the mob. J'zargo's major skills are: Destruction, Restoration, and Conjuration.
Anyways, those are my favorite followers to use for the 3 playstyles I play as. There are many more to choose from - mix and match them at your leisure. Just remember: choose one that complements your playstlye. It will make the game that much eaiser for you. Or, y'know, you could just go with Lydia, as does everyone else.