I was hoping I could get a list of them up the top here, if people reply with their experiences I can add what the bookmaker does to you when they close your account.
So please reply! and I will add your input to this first post, and credit all repliers as the source

If we can get a big list of bookmakers here it will be good to compare their procedures and for reference in the future.
Edit:
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I just want to add here as my post might have been interpreted incorrectly

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Stan James
Limits: - No, instant close of account and blocking of placing any more bets.
Account closing procedure: - They will close your account, honouring all open bets, and refund the money to your payment method
Closing Message:
All Stan James accounts are reviewed on a regular basis by our Trading team, and due to betting patterns on this account the decision has been made to close it.
I would make you aware that this decision has been made at the highest level and will not be reversed. Any open bets will be honoured, and any outstanding balance will be returned to you via your normal withdrawal method.
[Source: MichaelVanGunnawin]
Marathon
Marathon limits after ~15days, this bookie it's a mine gold, take advantages as much as you can.
Fastest payouts I have ever seen, Skrill transactions are almost instantly [Source: CBZ]
bet365
BET365 - they limit you to pennies very quickly, i am not aware that they close accounts however. They use Flash Cookies to track your online activity from the same browsing session, so delete these regularly using something like Piriform's CCleaner (this applies to most bookies). [Source: ArbAttack]
PinnacleSports
PINNACLE - do not limit / close [Source: ArbAttack]
William Hill
william hill- will limit you after 2weeks of arbing. I was allways try round stakes to 10. But limit comes. Limit is about 2-20€ per bet. They dont close account. You can then withdraw and move to next bookie. [Source: Mi_t_is]
Coral
CORAL - do not close accounts, but limit pretty quickly. They seem to apply limits by individual sports however, so if you are limited on Soccer markets for example, you should have a couple of bets on another sport where limits do not seem to apply! [Source: ArbAttack]
Coral limits you very fast, you can't place bets no more, I've spend around 5-7 days on both [coral and betvictor] before being kicked out - Payments received without any problem [Source: CBZ]
BetVictor / Victor Chandler
BetVictor (old Victor Chandler) the same - [limits you very fast, you can't place bets no more] I've spend around 5-7 days on both [coral and betvictor] before being kicked out - Payments received without any problem [Source: CBZ]
Betfred
bwin
betfair
BETFAIR - You are only limited by the liquidity in the markets. Betfair themselves will never limit you, as they are essentialy a broker, so the more money you get matched, the more commission % they make. [Source: ArbAttack]
betfair will limit you too if you arb on fixed odds. [Source: drhoo]
Betcity.ru
Betcity.ru limits you after 3-4 days to 22E(my case) and now, they are playing with my nerves, blocking my account and saying that I'm having 2 accounts and that they blocked it for 2 months and I need to send them a copy of my passport. Still curious how this will end, since I'm having money in the account and they haven't said a sh!t for almost 25 days [Source: CBZ]
etc...