I couldn't tell you the last time I touched a newspaper... oh, wait, it was a couple weeks ago when I was starting up my charcoal BBQ.
I found with buying my first house (current house in WY) that the online listings were terribly unreliable. For instance, my own place stayed on Realtor for many months after it was sold. Several are just plain not listed in the first place, and despite the MLS system intended to work in a "Live" fashion, it still relies on human realtors to input everything.
The BEST source, hands down, is a local Realtor. They have access to LOCAL MLS (that's a paid service, I haven't been able to find access to this service anywhere except through a Realtor), plus they tend to do walk-throughs of all the homes as they come on the market. We got REALLY lucky when buying from out of town by finding someone who has shown himself to be so far above the rest I've delt with that it's a shame he switched careers.
My wife and I are in the process of selling currently, and we only look online at other areas. I can assure you we will never pick up a newspaper to look there. I wouldn't waste my money on that venue (either paying them for something or buying their drivel... might just be because the local paper is nothing but an opinion column of the editor, and I don't like his opinion.