Learn to deliver grenades effectively
Grenades can be very effective weapons -- they can soften up the enemy for a push, finish off an entrenched and already injured foe, or provide cover where none is available. But to use them, you need to be able to throw them accurately, and know not to try throwing them when you're open to enemy fire. Aim above your target, depending on distance, so that gravity can drop the grenade down into your opponent. Lobbing is the key.
Use say_team/radio/voice chat to coordinate with your teammates
Use radio commands, or -- better still -- voice chat via a good headset to communicate with your teammates. The radio commands -- or in the worst, case just using the say_team command -- can help organize your team, but there's nothing better than being able to talk directly to your teammates and have them be able to talk back. If you're a serious Counter-Strike player, you should have a microphone and have your voice chat subsystem configured. Consider the difference between using the canned "Enemy spotted" radio chatter and simply saying, "One in the building on the left, and one sniping from the roof on the right." Voice chat can easily turn even a group of intermediate players into a well-oiled killing machine.
Use hud_centerid
Enabling hud_centerid prints the identifying string -- the text that identifies the person currently under your crosshairs and indicates whether they're friend or foe -- just under the center of the screen, instead of in the lower-left corner. This is a far better place for it to appear, since the center of the screen is where your eyes will tend to be looking in the first place. This helps avoid excessive unnecessary eye movements -- concentrate on the center of the screen.
Use hud_fastswitch
Enable hud_fastswitch in your client. This will allow you to select weapons without having to hit the trigger in order to select them. Every second counts; having to hit the weapons category key and then the left mouse button takes time, and sometimes it's time that you don't have. Note that hud_fastswitch won't help when you have multiple types of grenades; in those cases you'll have to select the type you want and then hit the trigger to select it. But for all other weapon categories primary, secondary, knife, and bomb (for the Terrorists in a bomb/defuse map) -- this will allow an instance switch. Sometimes a single keystroke or mouse click can mean the difference between life and death.
When climbing ladders, do so quietly
Normally, when climbing (or descending) ladders, a fair amount of distinctive noise is made; if you're using this to gain access to an enemy-controlled location, this sound can give you away. You can substantially reduce this noise by holding down the crouch key while moving up or down; this reduces the amount of noise that you make to about half: It's still audible, but it's far less noticeable than the normal volume. Particularly if there is background noise, such as gunfire -- hopefully provided by your teammates -- this can make a stealthy incursion much more possible. Another little-known tweak is that you can turn sideways on the ladder (so you're facing the side) and use the strafe keys to get some added speed when moving on the ladder. For instance, get on the top of the ladder, face off to the left, and then hold down the backward, strafe left, and crouch modifiers; this increases your movement speed substantially without making more noise. Crouch while climbing or descending a ladder; you'll make much less noise.
Use radar to locate both friendlies and hostiles
Your radar (when enabled on the server) is an absolutely invaluable resource. It locates your teammates relative to you, and even indicates whether they are above or below you, and by how much. Effective use of the radar goes far beyond merely locating your friendlies; coupled with close attention to sounds, you can use a process of elimination to locate the enemy as well. Use of the radar can also help you avoid friendly fire incidents; when you hear someone nearby, you can determine with the radar whether or not they are a friendly or a hostile. Use of the radar coupled with attention to sounds is a powerfully effective combination.
Stay out of water
Water is trouble for three reasons: first, you move more slowly when swimming; second, when swimming, your accuracy is severely reduced; and third, you make considerable noise when entering and exiting a body of water, and even when swimming (bubbling sounds occur occasionally). It's best to avoid water unless you have to, since it will put you at a disadvantage and let your enemies know where you are. Avoid water unless you have no choice.
Don't hop when covered by good snipers
It's common in first person shooter games for players to hop to avoid enemy fire by making themselves a harder target. But when under watch from very good snipers, hopping can in fact be counterproductive. In normal gravity, in the process of jumping, one's path becomes very predictable -- a good sniper will aim at the bottom of the parabola and pick you off as you land on the ground. To counter this, hoppers can perform mid-air maneuvers in order to try to make their paths less predictable, but in general (especially with the anti-hopping measures coming in 1.4) it's best to just avoid hopping when you know you're under close scrutiny from snipers -- it won't help you avoid getting hit. Hopping can help make you harder to hit, but not when your opponents are experienced snipers watching you closely.
Open grates and vents with knives instead of bullets
When on a map with destructible grates or vents, it's often best to open them with a knife instead of a gunfire. Even the most sturdy vents will fall to a knife thrust (the alternate attack), which is reasonably fast and will make considerably less noise than an (unsilenced) firearm. Particularly when coupled with timing -- open a grating when there is nearby gunfire to cover the sound -- a knife, or at least a silenced USP or Colt, can make an effective tactic for sneaking up on an enemy. A knife thrust (or at least a silenced firearm) is the best way to open a destructible grating or vent.