As many as you want! However, once you build up quite a few (read: 20,000+) the IM function will significantly slow down for you.
I had a good 22,000, and I could not load the page when I had new IMs. I ended up having to ask nil

to delete some of my older messages.

Try to keep your IM count below 20,000. ;)
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edited by tmpchaos 
last modified: 2013-09-20 14:08:45