I'd like to add a few comments in an attempt to be helpful.
1. Here is something unusual to watch out for. AOL and their free AIM offers IMAP mail. As the OP stated, AIM claims to offer unlimited storage. I've had AIM accounts for a few years and can confirm that all sent / received mail is still present in my account.
It is important to know that AOL, on the contrary, does not leave mail accessable for an unlimited time. I am not sure on this, but I believe the last I checked AOL deletes mail from their PAID user accounts after something like 90 days. Also, I saw where they sent messages to paying customers to "opt in" on something or sent mail would be disappearing after perhaps a shorter length of time. So, if you need to keep your mail for an indefinate length of time, go with the free AIM account if you prefer AOL type services.
2. I have a leased corporate server so I can set my own limits on my POP3 accounts. That said, I still prefer Gmail IMAP mail! Every time my account profile gets towards the specified storage limit Google just adds more GB to my storage space. I have also never experienced any "mail outages" when using Gmail. It always seems to be working.
Here is the best thing. I also use Thunderbird as my preferred e-mail software. Thunderbird works great with Gmail. As it is not uncommon for me to change computers, it is just a matter of installing Thunderbird, adding my Gmail accounts and then ALL of my sent/received mail magically appears. Since I work using several computers, I can always be certain that Gmail I send from work station A will always be present on netbook B, etc.
Gmail also does work with POP3 for those that do not need IMAP features. But, if you use POP3, then you need to manually back up and transfer your mail storage folders when moving to a new computer.