As others have stated, Marriott added the "suites not included" text a couple of years ago. But there is nothing that stops a particular hotel from upgrading someone to a suite room should they choose to do so. I would suggest that there are some steps that one could do that might "enhance" your chances though.

First, the longer the stay, the less likely one is to get a suite upgrade. Most of the times I have been upgraded have been on less than 4 night stays, though there have been exceptions. I would also guess that the higher one's elite status is, the better the chance. So stay more nights and get the better elite level. I have found it helpful to find out the name and email address of the general manager. Send the GM an email and let them know you are coming. Almost everytime I have emailed the GM, I have received some type of upgrade (though not necessarily a suite upgrade). So that will help. When you check in, ask at the front desk. It never hurts and the worst they can say is there are none available. There have been discussions in the past about whether checking in early or late is better, but I personally haven't found any correlation with check-in time.

And finally, have a smile on your face, be personable with everyone, and don't act like you are intitled to anything. And it can be especially helpful if you can get them to smile back at you.