I would like to remote into my Pi from outside my home network. The problem is that my apartment provides me with wireless internet and I can't access the router to enable port-forwarding. Is there any way around this? A dynamic dns service perhaps?
I would like to use VNC SSH and/or FTP.
I usually use Team Viewer to remote a station behind NAT without activating port forwarding like in your situation. You need to create an account on you team viewer application, and register your target station's team viewer to your account. When you are away, please make sure to always open your target station's team viewer and you will be able remote your target station by first login to your team viewer account. Once you are logged in you will have a list of target station that you have registered. Simply double click one of the list and you can remote your target station.
VNC or SSH will not be able to work behind NAT without activating port forwarding because the router will try to open it's own port instead of your target station.