Safety Tips: General

Safety is always a top priority no matter where your day will lead you.
Safety away from home is pretty much the same, no matter where you are, but being cautious never hurt.

Be Smart.
If you're travelling somewhere you don't know, don't draw attention to yourself. Don't stay in areas that make you feel uncomfortable or look shady. If you're travelling alone, avoid alleyways, dark streets and travelling at night. Do not pull out large amounts of cash, or hold large amounts of cash on you at one time. Avoid crowded areas like busy streets, strips, buses, trains etc. unless you absolutely have to. Only travel in marked transportation. Watch for pickpocketers. Keep important documents with you (passport, license, boarding passes etc.) as well as credit cards. Photocopy your passport in case it gets stolen or lost. Fill and label all medications before you go.
Lock up.
Lock your doors and windows at night. Locking your luggage, or hiding your valuables is also smart. Take advantage safes when they're available. Often they come so you set your own code. Also, don't put your home address on your luggage. Use the place you are sayings. Also, use covered luggage tags.

Dress Smart.
Don't dress provocatively, or unusual to that area. Don't bring valuable jewelery on trips, unless necessary. If uncomfortable with bringing wedding rings, get a cheap alternative at your local thrift store, or even Zellers or Wal*Mart. Not wearing rings at all is also an option. Wear comfortable shoes. Bring a money belt that goes under your pants, or a purse that goes across the body or hangs close to you. Do not bring larger than needed.

Eat Smart.
If you've never had something that doesn't sound good, or that has possible allergens in it, don't eat it. Drink bottled water, or canned drinks as often as you can. If tap water is necessary, boil it first. Check the internet to see if there is anything you should avoid at your destination (ie. Water in Mexico)

Here is a great article that has many of the same tips, as well as others. Be sure to read through each of them while planning your trip: http://ezinearticles.com/?33-Travel-Safety-Tips&id=31670

This may be very far fetched and not common, but reading these will make you think of a plan- just in case:
http://travel.state.gov/travel/tips/safety/safety_1747.html

Happy [safe] Travels!