Mostly online for me - depending on the part.
For example: I purchased some Vittoria Rubino Pro tires off ebay for $50. My LBS wanted $50 per tire!!!
Another example: I purchased some DEDA Newton bars and Bontrager X Lite seatpost from my LBS because if something went wrong or didn't fit right, I had a better chance of returning it. I could have saved myself at leat $60 buy purchasing them both online.
It all depends for me, but I will typically favor saving money rather than shopping LBS