The minimum fee possible is 0, however it depends on many different factors.

I suggest reading this article: http://bitcoinfees.com

Is there a risk that it never arrives? Could I respend it if it doesn't arrive?

I have to disagree with Cryptocat:
Yes, there is a chance that it will be stuck for a very very long time, especially if you are sending a tiny amount of BTC.
It is possible to double-spend the Bitcoins and the first one to be accepted in a block will come through.
(the same client won't let you make a second transaction, you could import the private key to a second one or use some program to edit a local client)

The transaction time is based on the integration of your transaction into a newly mined block.
Miners will prefer transaction with a higher fee (+some other factors like coin age, amount of Btcs,datasize), so they will include them first.
If there is a low number of transactions your transaction without a fee may be handled right away.

Btw: usual transaction fee of the qt-client is now 0.0001 (unless the Btc amount is made up by a lot of tiny transactions. If you collect dust from the free BTC sites and try to send all that the transaction will have a very big datasize)
You should be fine by using that fee.

The fee amount usually varies, but its never very high and usually isnt over 1%

If i am correct anything under 0.01 is about 0.0005 a fee
If you have a lot of small satoshi causing it to have a lot of memory or something you could get a fee of 0.0195 or something (meh o.o)

The default answer is now ฿0.0001/kb for Bitcoin-qt 0.8.2 and up. But, in reality, miners charge whatever they want. If evil mega-Corp buys a ton of ASICs (or miners collude) and controls nearly all the hashing power....they set the true minimum fee.

0.8.2 Release notes
===================

Fee Policy changes
------------------

The default fee for low-priority transactions is lowered from 0.0005 BTC
(for each 1,000 bytes in the transaction; an average transaction is
about 500 bytes) to 0.0001 BTC.

Payments (transaction outputs) of 0.543 times the minimum relay fee
(0.00005430 BTC) are now considered 'non-standard', because storing them
costs the network more than they are worth and spending them will usually
cost their owner more in transaction fees than they are worth.

Non-standard transactions are not relayed across the network, are not included
in blocks by most miners, and will not show up in your wallet until they are
included in a block.

The default fee policy can be overridden using the -mintxfee and -minrelaytxfee
command-line options, but note that we intend to replace the hard-coded fees
with code that automatically calculates and suggests appropriate fees in the
0.9 release and note that if you set a fee policy significantly different from
the rest of the network your transactions may never confirm.

Whilst it is *possible* it is actually in practice rather difficult to do (I tried once after making a huge mistake with fees doing a raw tx).

Any node that has seen the first tx will ignore the "double spend" attempt - making it virtually impossible to then do so after only a few seconds across much of the network.

Actual recomended fee is 0.0001BTC

Indeed, I used the same words than the post I replied to
That would be nice to find another word for this

For newbies: double-spending means here 'replace an old, stuck transaction which isn't accepted in the blockchain with a new one'