Kate

KDE 4: via Build Plugin

This can be used to execute the current file (if file permissions are set to executable and Shebang in first line is present)

Enable via

Settings -> Configure Kate -> Plugins -> Build Plugin

In the "Build Output" window, at the bottom of Kate, enter the following minimal settings:

Working directory = %d
Quick compile = %f

You might want to define a shortcut for this using Settings->Configure Shortcuts->Quick compile

KDE 3: via Plugin External Tools

This can be used to execute the current file (if executable)

Label:        Run (tm)
Script:       konsole -e bash -c 'cd "%directory"; "./%filename" ; read -p "Enter to close" '
Executeable:  konsole
Save:         Current Document

You might want to define a shortcut for this using Settings->Configure Shortcuts->External Tools