Can you have a bodyguard on The Elder Scrolls IV Oblivion

Sort of, if you join the dark brotherhood and when you get to the point of visiting the night mother, after that you get teleported back to the sanctuary, do the next dark brotherhood quest then go back to the sanctuary and there will be a new guy called dark brotherhood murderer talk to him (he will have a bow on his back) and say come with me, serve your listener and he will protect you. Hope this helps :) Also in addition you can get fellow guild members to follow you from the Arcane University in the Imperial City if you have completed the Mage's Guild path.