Since earning Platinum late last year, I've been about 50-50 on upgrades. Half the time, I get "upgraded" to a concierge-level room. The other half, I get upgraded to a junior or full suite. The best result was last week in Waikiki, when the Waikiki Beach Marriott Resort upgraded me to a full suite on an award stay for being Platinum.
The key, I've found, is the remind them at checkin that you want the upgrade. Often times they "upgrade" me to a concierge room before I check in. But I always ask if there are any suites available, and if they are, I've always gotten them.
When in doubt, call just before you check in and ask if they have any suites available to book for the time you're staying. If they do, thank them and tell them you'll call back. When you check in, if they claim there are no suites available, remind them that their reservations agents are happy to sell you a room, and therefore a room must be available, so you'd like that suite.
Remember, though, to be polite!