A side project I'm working on is a multi-player Flash-based side-scroller; as such it can run cross-platform on PCs but also on Android, games consoles and even iPhone/iPad using the right tools.
The nature of the game is designed to make it great for casual pick-up-and-play which would ideally fit smartphones/tablets, and would allow phone users to be playing against PC users.

But, I am trying to figure out how to do UI on touch-screens, in a way which doesn't make it a totally new game. For a start touching the screen obscures your view, and other things too. How might others approach a side-scrolling game (let's take the old duke-nukem or mario games as good examples)?

Hmm I'd first force the game to run in a horizontal alignment.
Then give the user the choice of using the either the trackball or accelerometer for movement. And have an action panel the user configure to either side of the screen to tap and use simple gestures for actions. A press could shoot, and slide could change to the next or previous weapon.

The downside of course is that it doesn't really allow for precise contols. So if you have lots of tricky jumping puzzles the mobile players might be out of luck.

Trackball? I'm not sure I know what you're referring to.

I like the idea of 'buttons' on the sides of the screen, or similar.

The trackball might not be not be available on all phones. My nexus one has a color changing track ball at the bottom, I just figured it was on most android phones.

Most Android phones lack a trackball, and it seems like only low end texting phones have keyboards, with exceptions like the G2 and Droid 2. Touch screen controls are the way to go, with other inputs as options if you have time to code them in. I bought a mini Bluetooth keyboard to use with my Inspire 4G for emulators, but for playing anywhere other than a table that's useless. Buttons on the bottom or sides of the screen work well if they're large enough. I've used that approach in one simple game, and another I'm working on.

Yeah, in my game I am doing the same thing with controls on the bottom sides. The trick I guess is to not display anything super important in those areas. And if you need to do a run-jump, good multitouch programming is required.

How many different actions can a player do? If the game is also for computers I can imagine that there's more to it than running and jumping. If the player has a lot of potential actions designing UI for a smartphone gets very difficult due to the size and number of buttons that would have to be on the screen. Looking at the size of the Droid screen, I can't imagine more than two or three buttons per side. Also, you should definitely keep any player info in the middle of the screen.