My first trip to DL was in Jun 98. I was attending a 5-day seminar at the
Disneyland Pacific (now Paradise Pier) so I was by myself. One afternoon I was waiting in line for Splash Mountain when I noticed a little boy (around 9 or 10 years old)working his way up the line. At first I thought he was just trying to cut in line, but when he got behind me he stopped. There were 2 girls (19 or 20 years of age) behind me, and they seemed a little surprized at the boy, but didn't confront him. I thought as long as he wasn't cutting line in front of me, I would keep out of it.
I've been in a lot of third world countries where pickpocketing is a way of life, so I generally stay aware of where my wallet is in relation to other people. I noticed that whenever I shifted from one direction to the other, the little boy would also move (i.e. he was basically trying to stay near my wallet). In crowds I hook my hands in my jean pockets and touch my wallet with my thunb. That way there is no way to get my wallet without me feeling it move. The little boy kept tracking my butt (i.e. wallet) for a few more minutes and finally I looked straight at him kind of hard. He then looked out into the crowd and I saw a hispanic man make a hand signal to the kid. The kid (also an hispanic) just disappeared. After he left, the two girls behind my started laughing and asked me how I knew the little boy was trying to lift my wallet.
So although DL (and WDW) are generally safe places with excellent security, never let your guard down because it only takes one thief out of hundreds of thousands of innocent people to ruin your vacation.
Fanny packs (especially if on your behind) are an excellent target for thiefs. They can unzip them
(or even use a razor to slice them open) and take things without people ever knowing it.
In heavy crowds, putting a wallet in your front pants might help. Believe me, crooks can be amazngly inventive when it comes around to stealing from honest people.