While I'm sure that people have had their strollers stolen at Disney, I think it is not that common. Most often, what I've heard of happening is that there's a case of "mistaken identity" where someone may accidentally take a stroller that looks like theirs, and even more common, the CM's move them around to make room for more (or move them out of areas are that are not designated for stroller parking) so sometimes you have to look around for it a bit. We usually wrap a brightly colored bandana around the handle so we could spot ours easier. You can use ribbon, or any number of things to "personalize" your stroller so it identifies it as yours. I've also seen it recommended here to put address lables on the frame underneath where people can't readily see it - that way if it does get taken and later abandoned (or you happen to spot it somewhere) you can prove it's yours. Personally, we've taken nine trips (all a week or more) to WDW with a stroller of some sort (ours aren't super expensive but they were still nice), no one has ever messed with them beyond reparking them in the same area. I've also seen quite a few really expensive strollers in the parks so if yours is that variety you wouldn't be alone. Personally, I think younger kids are more comfortable in their own strollers - they are not hard plastic, can recline for napping, have a better sun shade... Parents also find that their own strollers usually have more parent convenience features than the rentals - like a basket, cup holders, etc. Just some things to consider.
hth
