Does anyone know if the big time engines (like Unreal, Gamebyro, Crytek) require a splash screen on games that make use of their engine? I remember hearing that they do which seems odd since the amount of money they cost.

Depends on the specific terms of the license, most likely. I don't think it's unreasonable at all, even though they are expensive -- if they aren't marketed, nobody will buy them, and marketing them by associating them with the games they are used with is a perfectly logical method.

I don't think it is a requirement but, why wouldn't you want to have the splash screen?
With some games it seems to be benificial to show off which technology your game uses.

just wondering as I was getting mixed result and writing a blog post, located here, and wanted to see if I got a different reply from here, but again mixed.

I can't recall Oblivion or Fallout 3 having a splash screen for the Gamebryo engine although there are Logos for Gamebryo on the back of the box. If you select credits from the main menu of Fallout 3 it does show you logos for all the middleware used (there is a lot).
Well until you are actually in a position to be stumping up the cash to licence Unreal or the Cry Engine I think it's going to be pretty impossible for you to find out if you have to show a splash. At a guess I'd say it's on an individual basis.