So its now Monday the world over and the votes are all in at Bitcoin Bonus.  Here's the final list there:

zibit

ubitcoin

TriBit  (2)

Tiny-Bit

tidbit

tBit - pronounced tee-Bit; t as in one thousandth of a BitCoin

smilibit

nibit

Nibble

nanocoin

m฿

mint

Milth

millie(s)

millicoin (

millicent

milliBitty

Millibitcoin

milliBit (mB)  (15)
 
millebit

millcoin

MillBit

milicoin

milibit

MiliBit

miliBC

milbtc

MilBits

mil

Microcoin (2)

mic

mBTC og 1000-parts

mBitcoin

MBC (pronounced like the letters)

m1, 2m etc.

Little Penny Bitcoin

Litbit (3)

Kris

groat

Free

farthing

do bit - at this small size it's no longer a question of value but principles - what will you do in the world with a tiny little influence?

credit

Bity

BittyCoin

BittyCent

bitty bitlet (then 0.01 is a bitlet, then 0.01 is a bit, then 1.0 is a bitcoin)

Bitty (plural form: Bitties) (2)

Bitping

bitney

bitmillit

BitMillen

bitmill, bitmile(11)

Bitmi

bitly

bitli

Bitlet (3)

bithun

Bithou

BitDots

bitcoinmill

Bitcoin is very good.

Bitcoin atom

Bitchit

bitcent (2)

BitByte (2)

bitbit (4)

Bitbat

Bit-Tot

Bit-Mini

bit-hundredth

bit

BB

bantam bit

BajtCent

Amir

A bitpence

A bitk, pronounced bit-kay. Simple, short, and 1000 bitk would be one bitcoin.

A bitillion

1 Milicoin = 0.001 BTC

0,001 bitz


So with that, we had 15 votes for milliBit:  it is the winner, although it will likely be abbreviated down to be Mill/Mille as Gavin suggested.
zeploum was the first to suggest this, along with 'mille'    Congratulations!

I'm also awarding AntiVigiliate 5 BTC for his suggestion of Do Bit.  I'll likely use that at times in the hopes that it becomes an informal name for 0.001 BTC, the same way that we have crown, farthing, sovereign and guinea for Pound,  or Buck for Dollar. 

I like whoever suggested "hopefully 1 Dollar"!

Thanks for everyones thoughts and helpful suggestions.  Let the Network Effect take over from here and lets see what sticks!