I've usually had more than one roommate, but I have a strong opinion on laundry which wouldn't vary: I use it as an initial filter, because, at least for the kinds of apartments I have lived in, the condition of the laundry is the best single proxy for everything else I care about.

I wouldn't look at a place with no laundry or with coin-op. Laundry in the basement would make me suspicious and I'd need a lot to balance it out, like the basement being really clean and not accessible to anyone I didn't trust. Restrictions on the hours I could use the laundry (e.g. because of bad noise or vibration isolation) would be another major red flag as to both the condition of the building and the personality of the landlord.

If there's a good location in the unit (e.g. a dryer vent is provided in a logical place), permission to install my own is about as good as laundry already in the unit, though. That's how it was where I live now -- I got a cheap dryer off Craigslist.

My most/only useful piece of advice might be this: If you choose to provide laundry machines, make sure they are as clean and operational-looking as possible when you show the apartment.