This is the real rub. As soon as remote storage is a requirement, you start to need some kind of service provider to do it. This service provider could be anything from a purpose-built service to a generic storage service (think S3, Google Drive, DropBox, etc), to a co-located server, to a VPS, to a machine sitting at a friend's house.
No system will be perfect though. What if the internet connection goes down? What if the power goes out? What if the provider for the remote storage goes down?
The amount of storage depends on the camera's resolution and frame rate.
One of my cameras records 640x480 at 1 fps, saving movies at 7 fps when motion is detected. I end up using 1GB to 1.5GB per camera per day, depending on how much motion is being detected. The files saved are 7 fps videos for each event, 1 fps videos for each hour (24 videos), plus the event videos all stitched into one video.
For my purposes, this is sufficient. Other folks might want 720p or 1080p video, have more cameras, etc, and have correspondingly larger storage requirements.
What kind of retention do you implement considering those storage requirements? I mean, a simple 4 camera setup would be 4-6GB/day which is ~1.5-2.2TB/year.
No system will be perfect though. What if the internet connection goes down? What if the power goes out? What if the provider for the remote storage goes down?