I recently did a mailing to a lot of hotmail addresses and now all the e-mails I send out (from PHP by the way) don't seem to reach their destination. So I figure hotmail banned my url...
Is there any way to get rid of this ban so my e-mails will reach the users again (like activation e-mails etc)?
Is your domain really banned? Didn't those emails just end up in junk folder? If the former, then you'll really need to contact Hotmail. Either way, I recommend you to read this article to avoid ending up in junk folder or to get banned again in the future.
Are you using a mailing class like swiftmailer? I've found it solves most issues.
If your server IP is blocked by Hotmail, try using an alternate SMTP to send the messages temporarily. Maybe Gmail's SMTP? if you have a Gmail account of course. Don't abuse it though.
I am almost 100% sure that Hotmail will remove your IP eventually from the blacklist. Most services run a 48-72 hours ban; if they don't receive any more requests from the banned IP, it will get removed from the list.