Buy clothes when you get to your destination. You don't have to spend a lot, and the investment is well worth it, considering how effective it is for blending in in a foreign country. A tourist's outfit is usually the biggest give-away.
Consult your map before leaving your hotel room. Know your route. Referring to a map on the street or in public places is like pointing a spotlight on yourself as an easy victim. Carry the map with you, of course, in case you get lost, but keep it in a bag, pocketbook, or otherwise out of sight.
Carry your camera in a bag or purse. Having a camera at the ready makes you constantly conspicuous. Don't make it hard to get to, as you shouldn't sacrifice the opportunity to capture a great picture for the sake of blending in. However, having a camera dangling around your neck is like wearing a sign that reads "Tourist." Cameras are also common targets for thieves, and can make you a particularly appealing victim.
Buy a local magazine or newspaper and carry it around. The impression that you speak the language is helpful in both being less conspicuous and in appearing less helpless.
Avoid making hand gestures when traveling abroad. There are very few gestures that are universal, and it's likely that yours will look foreign. Beyond that, some gestures can have very different meanings in other countries, so an innocent move can actually get you in trouble.
Do some research on customs in your destination before traveling. For example, in some countries around the world, eye contact is avoided as a sign of respect. In other places, it's insulting to put money directly into someone's hand. Simple actions that contradict basic local customs immediately single you out as a tourist.