If you take a stroller, get a lock for it if it is a high-end one. On many rides and attractions, you will be separated from your stroller for 30 minutes at a time. Theft is certainly uncommon, but not unheard of. Also, any belongings that you will not carry with you should be locked as well. How to lock them is a different problem.

Note that a security guard WILL look through any diaper bags -- not enought to actually find anything dangerous, but just enough to make the sheep feel secure (security theater).