As I've said before, there are two types of Alfa pundit – those who have owned one and those who haven't.
The have nots tend to spout numerous pearls of wisdom about the cars' reliability.
I had a 2.5 v6. Great to drive, the electric windows all worked and the tyre wear wasn't at all excessive. On the other hand, the fuel consumption was excessive and it ate an air mass meter every twelve months and one day. The latter might have had something to do with the aftermarket air filter I'd fitted to it (Brrrrrrapppp! Brrrrrrrrrap!).
Older 156s have Magnetti Marelli electrics, which can be problematic. Alfa redesigned the 156 to take Bosch electrics from around the 2000 model year and these cars are the ones to go for, all the Italian flair without the gremlins.
You need to be on the button with servicing and cam belts as others have said, but that is also true if you're buying a sixteen valve Volkswagen Golf or a Ford Zetec. Also suspension groans shouldn't be ignored, part of the servicing routine is to keep replacement of bushings and track arms spread over the lifetime of the vehicle. If the previous owner has neglected this, then you're in for an expensive service. Again, the same is true of a good many multi-link designs.