I've seen some confusion over iCloud's Photo Stream feature and whether it allows your photos to perpetually remain in the cloud. Apple could do a little more to help clear this up, but until then: Photo Stream and Shared Photo Streams are two related features that have different rules, and yes, there is a simple, official way to permanently store and share your photos with iCloud.
The TL;DR Version
My Photo Stream is a running tally, your latest 1,000 photos shot on iPhone or iPad, not permanent storage. If you want to keep these photos, you must download them from Camera Roll on your devices or from Photo Stream using apps like iPhoto and Aperture on a Mac, or with iCloud Control Panel on Windows.
Shared Photo Streams are permanent iCloud albums for storing photos and videos that can sync across all your iCloud-enabled devices. Optionally, these streams can be shared with friends or the public, and you can allow friends to collaborate and add their own media. Shared Photo Streams have a few limits that Apple recently relieved somewhat, but photos in them do not count against your total iCloud storage and will remain there as long as your iCloud account is active.
If you want more details on My Photo Stream and Shared Photo Streams, keep reading.
My Photo Stream
My Photo Stream is a running tally of your latest 1,000 photos, not permanent storage. It's meant to be an effortless way to get your latest party or vacation photos from last week onto an Apple TV, Mac, PC, or other iPad for downloading, editing, or sharing. It is still up to the user to download Photo Stream photos (or original Camera Roll photos) and keep them for permanent storage, or to use Shared Photo Streams; more on those in a moment.
On a Mac, iPhoto and Aperture are good for downloading and permanent, offline storage because Photo Stream support is built right in (plus, for the mobile pros in the audience, Photo Stream does support RAW files across all devices. All other large images get resized to 2048 x 1536 pixels). You can also enable options in iPhoto and Aperture preferences to automatically import all Photo Stream photos. If you go with this workflow, be sure to run these apps often enough so Photo Stream doesn't drop any photos before you catch them.
On a PC, enabling the Photo Stream option in Apple's iCloud Control Panel for Windows will automatically download all My Photo Stream photos to C:\\Users\<user name>\Pictures\iCloud Photos\My Photo Stream.
Shared Photo Streams
If you want to use Photo Stream as a permanent, multi-device, iCloud-powered photo storage and sharing service, you're looking for Shared Photo Streams (even if you're not looking to share them. I know, it's a tricky branding challenge). It's worth noting that, unlike My Photo Stream, Shared Photo Streams support videos and, optionally, allowing subscribers to collaborate and add media, as well as sharing with the public. Like many people, I hope Apple will add video support to My Photo Stream.
You must manually create Shared Photo Streams and manually add photos and videos to them whether they are already in My Photo Stream, your Camera Roll, or, if you're on a Mac using iPhoto or Aperture, from other sources like apps or the web. Like My Photo Stream, photos added to Shared Photo Streams do not count against your total iCloud storage (however, it sounds like videos do; Apple needs to clear this up too). However, the great thing about Shared Photo Streams is they do not disappear and never automatically dump older photos to make room for new ones.
Shared Photo Streams do have a few limits on the number of total streams you can create, how many photos and videos each stream can hold, and, if you choose to share a stream, the number of total subscribers and invitations you can send per day. Apple recently raised these Shared Photo Stream limits (hat tip to Shawn Blanc), and they seem pretty reasonable for most typical users. I wager that, in time, Apple will raise these limits again, hopefully sooner than later.