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I have the opposite, the bearded bloke in the dir. and Fallout boy on the desktop and I think it's always been like that on every install for me. (if memory serves me right)
Found this on NMA, thx to Sander for posting it:
"It's dependent on the icon size setting. So, change the icon size back to normal and it'll change back."
I did a trial in the folder and it worked there, I have the bloke with the beard if I have "miniatures" or the one below (unsure what it's supposed to be in english), but if I change to "icons" I'll get the Fallout boy in the folder as well. (and the same for desktop icon size, I changed to large and the beard appeared :))

So how do you change the icon size back to normal? That does explain other odd icon problems I have been having with older games.

In windows XP you can right click on the icon and go to properties, there you'll see an option to change icon.

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In XP (since I have Swedish I'll translate and guess, prob. won't be the right names though), right-click on desktop, choose the fourth tab (may be "appearance") and choose "effects", in it you'll find "use large icons", unmark it.
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This won't work, he'll get the same icon that's showing, it deals with the icon size, the 32x32 is the Fallout boy, the 48x48 is the bloke with beard.
There's however a way to go around the problem, if someone wants large icons:
1. get IcoFX (it's free)
2. open the fallout.ico in the program.
3. click the 32x32 - 8 (Fallout boy icon)
4. in the toolbar of the program there's a windows flag, click it, I chose all the available colours but I doubt that's needed.(the original options should be enough, it's the 48x48 XP and 256 colours that's needed)
5. in the new window that popped up after the above action, click the 48x48 - 8 or 48x48 - 32 icon
6. choose "file" -> "save as" and save it in the FO folder under a new name.
7. create a shortcut of it and move the shortcut to the desktop, rename it to Fallout or what you prefer and it should work.
You can't just save the icon on the desktop, FO will complain about you not having the CD, so you'll have to make a shortcut of it.

Thanks all.
First I am using Vista-64, but changing all my icons did work fine in this manner: right click on desktop -> view -> classic icons. Note mine was originally set to medium icons. Warning when I went to large icons (just for yuks and then back it spaced my icons rather weirdlly. However, with my current desktop classic icons are a bit small so I will play with the icon editing portion of it. But now I have an explanation why my older games sometimes have ugly icons, which was an impoderable mystery.

Good to hear it worked, yeah you'll have to edit the icon into 48x48 to get medium size, at least I suspect that's medium size. (I've always used 32x32 myself it seems like, since I've never had the problem :))
It's good that the icon mystery has been solved at least and GL with editing the icons.

The bearded guy is there on both Fallout 1 and 2's exe. It been the case since the original release of the game. Guess its one of the developer or something.
Yeah, either remove the icon or if you are using Vista, GOG.com's version adds a nice high res icon into your games folder. So just use that. =)

Thanks for pointing that out - the "box" icons are a bit more interesting.

Good call on the high-res icon in the game's folder! Thanks :)

Its Tim Cain - one of the original creators of Fallout. It was meant as an easter egg : ).