Is there a cloud service like Dropcam, but the video can come from anywhere? I want a service that provides the 7 days of cloud video storage, the app, and the web-based video player with time lapse and DVR-like features.
This might look like a software agent that you install on an old PC with a webcam attached.
There's a lot of options and implementations.
For cloud services there are foscam cloud, camcloud etc. They require you to open a port on your router ( kind of defeats the ease and security of dropcam type service.)
For a home server there are a bunch of options. Blue iris I think is a big one and there is sighthound.com
Good luck