The ones that I had on my laptop (I had a Flip for a while, and before that a Very Small Videocamera -- possibly two -- and of course the usual still-camera-that-takes-short-video stuff) I could upload to Flickr. Alas, Flickr will not do everything, and attempts to convert 3GP [eta: 3g2, actually?] stuff (not from any of my phones, but from some of the kids' aides at the preschool) ... turned out really weird and wrong in ways that sounded like the problems Flickr had with that format back when they still converted it. Also, Flickr has a hard enforced 1.5 minute play time limit -- it'll silently truncate anything you upload that is longer than that. I knew stuff longer than the official limit (30 secs?) was going through and it took me a while to realize what was happening, but I was able to confirm this is Known Behavior elsewhere.
So that left me with two problems. (1) The Flickr iOS app in its current incarnation will not upload video of any format or size and there's been no word for months that that functionality will ever return. (2) What to do with the long videos that I cannot store on Flickr.
I went over to Vimeo, where I've had a largely inactive account for about five years (but they oddly haven't erased any of my files, thank you Vimeo for being very nice) and looked over their pricing and features. Then I looked at who owns them, and I thought for a while about their TOS and what you have to do to ensure access to your original file if stored with them and concluded that I wasn't as comfortable with Vimeo as a video archive as I am with Flickr as a photo archive.
I'm waiting to hear back from some friends about a reasonable second choice, but in the meantime, I figured I might as well see how Google Drive works. Again, I use them already for text files, and their pricing, TOS and ability to retrieve original file seemed like a trustworthy solution. Playback seems okay, and I didn't encounter any delays in uploading.
There's a Google Drive iOS app, which I had already downloaded to access my Google Docs notes (where what I used to have in EverNote went after I had a temper tantrum about syncing conflicts and cut-and-paste issues). Does it upload video? Oh, yes it does! Very fast, too! I'm off to see how playback looks.
ETA: Looks fine! The worst aspect of Google Drive for videos is the lack of a thumbnail, so it is helpful to name the files something informative. I'll go with this solution unless something particularly compelling comes along. Because the free storage is 5 Gigs, and I'm currently only using 2 (and that from recent uploads), I may not have to pay anything for this, however, the pricing structure seems fine if I do need to pay for additional storage (altho that would likely motivate me to do some more careful editing of what I decide to keep).
ETAYA: I'm going to tentatively say that I've uploaded all the videos. But I suspect I'll find more somewhere. And I still have a quarter of my free google drive storage left.