There is a limit, it's called carry weight. When you are carrying more than your limit allows you can't run, sprint, or fast travel unless on horseback. In older TES games your character couldn't move at all while over-encumbered.
I like to only grab things that have a value-to-weight ratio of 10/1 (1 weight unit being worth 10 coins) or higher. Then I take it back to my home and organize it between stuff I'll need later on for that character (like good potions, ingots/ore for blacksmithing, or soulgems for enchanting) and crap I won't be needing like extra armor, weapons, misc items. Then I'll sell the crap when the shops open or just hoard them and when the list gets big, I'll make rounds to the different cities, selling til it's all gone. If the list of excess items gets huge I like quicksave and then drop it all on the floor just to look at the pile it will make, then reload.
also the title immediately reminded me of this http://www.youtube.com/watch?v=Vcx6UbMCtfI.