Every trainer has a game version in its description, so check it against your own actual game version - if its not the same, it will not run as the trainer may or may not find the game, if it is a cracked game - it can crash, if it has different version - some options can work - some not.. or it can just crash the game (even you heard Trainer Activated - it doesn't mean that it will work if the game version is different from trainer.
So, play legit games and u will get trainers to work ^_^
P.S. Sorry for my bad English and I hope you got the idea.
Speaking about run as Admin - you give permissions to a program to access the process which otherwise would be denied by windows itself as a security mechanism. There have been cases where some games just crash on certain system configurations - usually with illegally downloaded games, but there is a possibility that it could crash with legal ones as well. Try always to install programs which comes with the game such as DirectX, VB2000 or other software it provides, even if you have the newest DirectX - sometime they include customized one and this can prevent the game from launching properly.
Hope this helps, try some running the game without trainer - if it doesn't work, its not the trainer - try installing from the installation disc software like DirectX.
If it works, then check trainer/game version - if it is a match, then the question is - is the game legal or illegally downloaded?
As for most users the trainers work great without any problems (Thank you CH for the hard work).