I may take an evening flight out of Rome. Does anyone know if hotels would hold my luggage during the day (after having checked out) so that I can do my sightseeing and come back to the hotel to pick up my cab from there?

Can't imagine a hotel that wouldn't.

I haven't done so in Rome, but in other European cities the hotels have held my luggage for me till it was time for me to go. One German hotel even let me use their free internet access after I had checked out!

Agree that I can't imagine a hotel that wouldn't. We did this in Aug. 2001 in every hotel we stayed in. Rome, Milan, Verona, Venice, Ancona. No problems. Don't necessarily expect them to keep the stuff under lock and key, and to feel responsible for it, though. Some do; some don't. Still, we had no problems.

Pretty common to expect. I've got to agree, most do. My experience is only Venice, Paris (and various spots in Mexico) but most front desks have a closet or somesuch where you can drop you bags, either if you arrive earlier than check-in or for the day you are departing after check-out.