For Textmate there is a command line tool, mate, that can be installed. Once installed you just use mate <file> to open that file in text mate.
For application that don't have a command line tool, you can use the open command with the -a flag and the name of the application. i.e.
open -a iTunes
This also works for TextMate:
open -a "TextMate 2"
The executable file is located in the app's Contents/MacOS subfolder, so for TextMate 2, it would be:
/Applications/TextMate\ 2.app/Contents/MacOS/TextMate
But if you run it from the command line like that, it will hang the shell until the application is quit (on certain older OSs; this was resolved as of 10.8) If this happens to you, put an & at the end of the command to background the process. Such as:
open -a BBEdit &
