Here are submissions so far, in roughly reverse alphabetical order:

zibit

ubitcoin

TriBit (2)

Tiny-Bit

tidbit

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

nibit

Nibble

nanocoin

Milth

millie(s)

millicoin,milicoin (9)

millicent

milliBitty

Millibitcoin

millibit,milibit (15)

Millebit

millcoin

MillBit

MiliBit

miliBC

milbtc

MilBits

mil

Microcoin

mic

mBTC og 1000-parts

mBitcoin

m1, 2m etc.

Little Penny Bitcoin

Litbit

LilBit  (2)

Kris

groat

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)

bitty

Bitping

bitney

bitmillit

BitMillen

10 satoshi's

BitMill, Bitmil - (10)

Bitmi

bitly

Bitlet, bitlit (4)

bithun

Bithou

BitDots

Bitcoin atom

Bitchit

bitcent (2)

BitByte  (2)

bitbit (3)

Bitbat

Bit-Tot

Bit-Mini

bit-hundredth

bit

BB

bantam bit

BajtCent

Amir

bitpence

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

bitillion

I'd encourage people to look over all of these and continue the discussion about what is the most useful name.  Spelling isn't so relevant for now, its the phonetic sound I'm curious about, I've doubled up those suggestions that have the same sound.