Excluding my "regular," the PHT, where I never ask -- being quite content with the Park room -- I'd say my rate is at least 50%, maybe even better. But I have found that I HAVE to ask, they never seem to do it on their own. Domestically, 1-800 CHECKIN will usually try to help except when you get those few unhelpful agents who allege they cannot call the hotel.
Unsurprisingly, the probability of a suite upgrade is much lower on a long stay since the hotel doesn't want to commit for a long time. There is also one hotel, at the Hyatt Sacramento, where I think the corner room was better than the suite we got once so I wouldn't ask for a suite next time!
Suite upgrades are one of the main reasons I think being a diamond is worthwhile.