I like MobileMe, especially for the FindMyiPhone feature (which I've used a few times) but it could use some competition, especially in terms of price. Ironically, before I became a full-time iPhone app developer, I worked for a software firm in the printing industry. We partnered with Ricoh and in that capacity, I beta tested their quanp service. Similar to MobileMe's iDisk feature, you can upload and share photos and files such as PowerPoint and PDF documents.
quanp is now available for the iPhone, and doing quite well (#2 in Japan). You can upload existing photos and videos from your camera roll, or use the app to take pictures and videos (iPhone 3GS and iPhone 4) and upload them. quanp holds its own against iDisk in several ways. First, it's free and that's always nice. Second, you get 10GB of storage and can send large files, up to 500MB to anyone. They receive an email with a link to download the file. With iMovie on the iPhone 4, this could be useful. Obviously, this printer manufacturer is hoping you will use quanp to share printable documents and photos, and print them on Ricoh printers.
There are more features in quanp, beyond iDisk capabilities. Similar to Bump, you can 'Flick' files to local iOS users using Bluetooth! Also, there is a Voice Memo feature so you can record audio notes easily and of course, share those files.
The name doesn't flow off the tongue, but it comes from "quantum paper". Hey, I guess all the good domain names are taken.
quanp is a nice app and service, and the price is right. It's been in beta for a while now (about a year) but you can tell they've paid attention to details. I would like to see it become a Universal app, with iPad support built-in, as I think that will be a better device for creating or viewing spreadsheets and other content you might want to share.