I poked around, looked at different thingimagigs, and eventually found this. This is a system with space for two hard drives that runs an OS specialized for data storage. It should be able to wirelessly stream data, allow me to access everything on it, and do some other things I didn't think of like connect to printers, speakers, and external hard drives. This one costs $200; It comes without any drives, yet has room for two. I looked on Newegg, and found these WD Caviar Green 1TB hard drives. Two of these for $62 each, stick them into the nice NAS, arrange them in RAID1 (basically, so that despite there being 2TB of available storage (2x1TB), only 1TB is usable; the 2nd TB is used to make a backup of the 1st TB, in case one of the drives dies), and I'll have a safe way to store all photos, videos, music, and whatever else I want, make backups of my laptop, and access everything wirelessly, and if they release a version of their app for WP7, I'll even be able to do it from my phone.
I also looked at some other offerings; Netgear had something similar, but reviews were significantly worse. Qnap was mentioned by a friend; they seem to have an almost identical range of NAP's to Synology, but their model at the low-end of two drives is $40 more, and they seem less popular (no Wikipedia article!); otherwise, the tech-specs are amazingly similar. I also looked at offerings from WD, Seagate and Buffalo, but their networked drives seemed thoroughly inferior.
Basically, if someone has any problems with what I'm doing or has any recommendations, I'm asking for it, because I just had the idea to do this today and did all of the research in the last few hours. I looked at some web services for backups and such, but Carbonite lacked streaming capability, and everything else was pretty expensive; I believe Amazon charged just about the equal of the number of gigabytes you use per year (so for 1TB, that's $1000/year), Microsoft Skydrive seemed relatively limited and I couldn't even find an "expand storage" button, and other services I thought of were too limited to fulfill all of my wants. It would likely have impressive integration with WP7, but, alas.
None.