For Counterstrike there is a huge number of aim maps on the workshop, designed to help you practice your aim. Some are just mods to only count headshots, but some are great little parcours with separate corners for different techniques.
The ones i use are called aim_arise and HS Aim Training (you'll need to read their store page to know how to spawn and despawn bots and such)
http://steamcommunity.com/sharedfiles/filedetails/?id=189253163
If you're playing counterstrike, play some games on casual every once in a while, because it gives you a freezecam of where the enemy that hit you came from. Remember this, because most players will re-use tactics that have worked the round before. Try and use their tactics against them, especially from players where you find yourself thinking 'where the hell did he come from?'. Try and figure out what route they took, and csgo makes this easy for you with their theatre mode.
Every once in a while, spectate some high ranked matches. You'll notice that there can be several hundred spectators watching the stream or the event in-game. They're watching to learn new tactics and new spots aswell.
For any of the others, i look up skilled players on youtube. Look at the video once, if it's a tutorial then you can leave the audio on, but otherwise turn off the audio. Now try to look for the little tricks they use and where they stand and look. Sometimes it seems like they are standing just randomly, but there will be always something good about that paricular spot, either for the viewlines it offers or for it's protection against spies or snipers.
Try to find them yourself by watching where other players are standing on the map, stand in their stead for a moment and try to see what they are looking at. Try to aid them by covering the corners they can't see, so you'll become a two man wall of bullets.
This ofcourse applies to shooters mostly, but i don't play any of the others you pointed out. At the time i was at my best at CSS, i only played CSS. This is to stimulate muscle memory to do some things for me. Like quickscoping or just watching corners, you can never know at what height the enemy's head will pop out, so you'll need muscle memory to aid you in quickly finding your mark.
Last tip : Don't mess with your mouse sensitivity, it deletes all your muscle memory and you'll find yourself shooting at walls a lot.