I don't know if cruise ships have safes in the rooms, but they're bound to have somewhere secure. Leave everything you do not absolutely need there when going visiting countries. Take as little money as you need and maybe one bank card.
I think the biggest problem in those areas are pickpockets and bag snatchers, so get a money belt or something else where you can keep your valuables under your clothes. If you have a bag keep a good hold of it, if it's a backpack wear it on your front (not on your back over one shoulder). Better not to carry a bag at all if you can.
If you carry a wallet keep it in your front pocket, but keep it as empty as possible.
Try not to look like a tourist, don't flash large amounts of cash -- go to the bathroom to move cash from your money belt to your pockets if necessary. Don't wear expensive jewelry or watches, small point and shoot cameras are better than the big SLR ones, but if you have a big one consider carrying it in a non-descript bag and only taking it out when necessary.
Be aware of your surroundings, particularly if people are doing something odd to distract you or trying to invade your personal space. Pickpockets I've experienced in western Europe tend to either be fairly blatant -- they come right up to you on some pretext and just grab what they can, or they have someone distract you while someone else grabs your stuff.
But also, don't worry too much, just minimize what you can potentially lose and be aware. As I've said before here -- you just need to look like a less tempting target than the other tourists (terrible, but true), so the mere fact that it looks like you're paying attention to your stuff will make many pickpockets just move on.