You don't need to play online.

you do not. 

Indeed like the 2 previous said, you don't need to be online, but you are missing a LOT of features of the game if you do not play it online.

No you don't.

" You don't need to play online. "

" you do not.  "

" No you don't. "

Nah but if you don't you'll lose the certain messages left by players, which often have helpful tips, and the bloodstains which show you how people in that area died, most of them are useless I find, because it's often out of place with the player backing away from combat then dying, so it's all misplaced help and it just makes you tread cautiously, even though you should be on this game. I'll also make the assumption you're not looking for co-op or anything so I wont mention that.
 
So overall, you don't need the interwebs you just miss one occasionally useful feature, but looking at a guide here and there will probably be necessary anyway, to utilize some of the items you find.

You don't need to be online to do a lot of the stuff - in fact if you are attempting a 'perfect' WT and 5 BP run through it's recommended you stay offline to minimise the chance of getting invaded and affecting the WT 
 
HOWEVER 
 
If you are just doing a standard run through, i'd recommend leaving it online, once you've built up a decent PVP type character black phantoms invading can actually be beneficial (seeing as you get all their souls for killing em), and leaving messages around is a good way to get your health regenerated, also taking on a couple of blue phantoms to roll with maximises your chances of success.

Yes, playing offline is a must for world tendency. In all honestly, if you care about tendency at all in your game I would recommend keeping it offline while you are working on a particular level. (wtb 1.05 to fix that shit)