I was assigned a housecarl doing the Whiterun quest line. What exactly are the benefits? I typically prefer to run alone but if the housecarl offers some buffs other than extra storage space I might keep her along.
Your housecarl (in this case, Lydia) will fight along side you and will essentially offer you an unkillable (except by certain important NPC's, or yourself) meatshield while also providing extra damage and storage.
It's not necessary to bring her along, and can actually sometimes be annoying, but if you need a little extra help, it's wise to let her tag along.
Your NPC followers cannot be permanently killed by any standard enemy attack (or trap), outside of certain quests that involve them. However, melee characters like Lydia have a nasty habit of wandering in the way of spells, arrows, and your own mighty axe swings at inopportune moments, and YOUR abilities DO permanently kill them!
There is also no built in option for turning off friendly fire--a pity when a firestorm is exactly what's needed.
I have found that Lydia also has a nasty habit--if I accidentally hit her twice in a single combat--to aggro onto me instead of what I'm fighting, swiftly beheading me with the very weapons I crafted for her defense.
There are other followers, including mages and archers, who will stand back from combat (as long as you don't let them carry any weapons) and reduce the frequency of these messy service terminations, and subsequent game reloads.
I've since picked up Faendal, dubbing him Knight of the Glorified Pack Mule and Sir Dragonbait, titles which he lives up to well--or, well, you know.