I've had as many as ten. I am now down to two. One that I actually check throughout the day and another I use when signing up for CPA offers or when I need to send other spammy stuff.
Yahoo says that they don’t recommend it, but that you can have multiple accounts (though they probably have something in their ToS against having multiple accounts for certain purposes, like spamming). I have two accounts on Yahoo, with two IDs and so forth. I don’t know about AOL or MSN.