(warning: haven't actually read AUP.)
I was young, naive, and trying to set up my own mail server. Ended up creating an open SMTP relay instead.
Received a phone call within 15 minutes of successfully testing my mail server! They were calling to tell me they suspect a computer in my house has a virus. I chatted with support for a while and we eventually figured out it was my mail server.
They were rather pleasant about it actually, they explained that it doesn't necessarily violate their AUP but it's hard to configure a mail server correctly.
I'd later learn that since my IP address was from their dynamically allocated pool: most popular mail servers would reject my messages as spam anyways.
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This was with TimeWarner cable about 7 or 8 years ago.
Plus I just like having my data here, and not somewhere where I have no physical access.
They block port 25 to prevent open relays on their network (i.e. someone sends a forged email, the SMTP server does no authentication, and just forwards it on to the destination).
This requires that your mail provider supports that port, of course, which is unfortunately not always the case.