Not just a phobia, general scaredy cats!

[PigLickJF]

If it's your character (whether you're GM or player), why bother assigning a penalty? Just volunarily fail all saves.

PigLick

[RoadWarriorFWaNK]

i would never play a character like that. What's the point of adventuring? just stay at home where it's safe.

[PigLickJF]

They get forced into it, or they force themselves.

Exactly. Monk as mentioned above is a great example. He is scared of just about everything out there, but he is still driven to "adventure by wanting to find out the details of his wife's death, to regain his position on the polics force, and generally by not being able to pass up a good mystery. It's a great character and, if done well, could be a lot of fun (as evidenced by Monk, which is a great show). As mentioned, though, it could also get pretty annoying (both to yourself, and the rest of your group), so it could be tough to pull off.

PigLick

[Shaved Monkey]

I wouldn't worry about applying penaltiess for cowardice. It tend to come out in the role-playing itself by avoiding dangerous situations and not being curious or even driven.