Follow your teammates' lead
In a team-based game, it's important to follow the lead of your teammates that are nearby. If your teammates are waiting in ambush, you should wait in ambush too instead of rushing out and giving their position away. If you're following some people who are clearly trying to be stealthy (by walking instead of running), you should be quiet as well, or otherwise you undo their attempts to not be detected. Even when you're dealing with players who are far less experienced than you, doing things together as a team will benefit your whole team.
When sniping known enemy locations, line up and zoom, and then strafe out of cover
When you're sniping, you will frequently find yourself facing off against other players -- possibly also with sniper weapons -- who have either directly spotted you or know the general area in which you're sniping from. When it's snipers vs. snipers, the first to get off the accurate shot wins. When you know the general area of your victims, instead of walking out of cover (where you yourself can be shot), zooming, lining up, and firing, try short-circuiting the process: Instead, when still behind cover, zoom one level and then step out. If you're aiming right, the enemy should be within your line of vision, at which point you can line up, possibly zooming in another level, and finish him off. This can substantially reduce the time you're exposed to enemy fire. Particularly when the other enemy is already out of cover and is waiting for you to pop out again, this can give you a fighting chance.
Always buy defuse kit (Counter-Terrorist)
On bomb/defuse maps, it's in the best interests of the Counter-Terrorists to always buy a defuse kit. In previous versions of Counter-Strike, it was fairly expensive, but in 1.3 and up it is only $200, the cost of a flashbang. You should always go out of your way to pick up defuse kits that are lying on the ground due to fallen comrades, as well. Always get the defuse kit. It's a steal.