Update: Apple now allows you to share your Photo Stream with others. More info on the official Photo Stream page here
At the moment no. The only way to access your stream is from a Lion Machine using either iPhoto or Aperture, or from another iOS 5.0 device with Photo Stream enabled.
I am not entirely sure if Apple is going to allow a sharing portal, however at the moment I take the images I want to share and upload them to Flickr through iPhoto once they are in my Photo Stream.
I suspect they currently use Photo Stream as a personal backup and sharing solution between devices, and not global sharing.
Photostream will store the previous 30 days worth of photos automatically. That means, every photo you take on your iOS devices will be sent to Photostream, but only the last 30 days worth of photos will be available there.
If you enable 'Automatic Import' of Photostream in iPhoto (Preferences > Photostream > Automatic Import) then when you launch iPhoto, it will automatically download a copy of any photos that are in your Photostream, and automatically create an Event titled: {MMM YYYY} Photo Stream (eg. "Jul 2012 Photo Stream")
This Event will be automatically kept up to date, as long as iPhoto is open long enough to sync everything required (depends on your connection).
In effect, as long as you open iPhoto once every 30 days and leave it open long enough for your Photostream to be imported, you should never have to manually import a photo from your iOS device at all.
As for removing items from your Camera Roll on your iOS device, as long as you see that they are present in Photostream (or in iPhoto), then it is safe to delete them from your device. (There is no way around this but to do it manually as far as I know.)
Currently, Photostream does not support videos. To import videos, connect your iOS device to iPhoto and import these manually.
As a side note, in order to keep some photos on the device, you can create a smart album in iPhoto along the lines of "Photos taken within the last 30 days" or "Photos rated 4 stars or more", and configure iTunes to sync these to your device. That way, you can be sure that no matter if you clear your Camera Roll on your device, or delete certain photos, you maintain some convenience.
Best Answer
As outlined in this question, a workaround does exist, but it's ugly.
You'd need to run a virtual machine running Windows (I'm not sure if you could do it with Wine, or if you'd need an actual copy of MS Windows (which is much more expensive than $16). You then download iCloud Control Panel from Apple and install it on your virtual machine. Then, you can use it to send photos to iCloud.
So yes, it can be done. But you're likely better off spending the $16.