Do only SLR's have a wide range of available apertures?

I'm looking for a new digital camera, but would like to have more control over the options. Is there a compact camera that has an aperture of say, f/16?

Okay, so I'm interested in the Canon PowerShot S3 IS, and it lists an aperture range of f/2.7 - f/3.5. So does this mean these are the only options or is there a smaller aperture availabe?

Your question is a little bit strange. Most point and shoot cameras, even the throw away ones probably inherently use a f/16 aperture. It would be probably the most common aperture used to capture a lot of background info in a landscape picture. An f/16 aperture isn't really getting creative. Geting creative would be say to make sure the camera has a real optical zoom of about 12X..equivalent to about a 400mm lens with a really nice lens, with say a f2.8 aperture lens, and has the ability to select film speeds...

Thats when you start really having photographic options.
typically most cameras with these features will cost about 500-800 bucks these days. You don't need a $2000 digital SLR.

Well f/16 is a small aperture (its a ratio, so the larger # at the bottom means small value). Most P&S cameras that have full manual function (or aperture priority: Av) will allow you to go down to f/16, f/32 etc. The trouble is getting the widest aperture (or the smallest # like f/2.8 of f/4) with a P&S zoom lens.

The Fujifilm S5000/6000/9000 series of cameras have full manual (and Av). Even the Canon G7 series has this feature.

One way of knowing if a camera can adjust aperture is to quickly look at the dial on top of the camera. If it has M, Tv (shutter priority), P (program) and Av on the dial along with the green box and other icons like (portrait, sports, party, landscape etc) then the camera has a lot of manual controls.

Off course I am assuming you know that the smaller the aperture (f/16, f/32) the MORE light you will need to take the same shot. And so you will have to use the flash (it will pop up in the Av or P mode when you set the aperture) or will need to be manually popped in the M mode. And sometimes the shutter speed for a given aperture/ISO setting is too slow even with flash to stop motion.

Most point and shoot cameras have the ability to stop down to f8, but I've never seen one that would stop down further.

Because of the short focal lengths used on point and shoot cameras, f8 is actually a very small aperture, very close to pinhole sized.

Because of a phenomenon called diffraction, point and shoot cameras would not be very sharp if they could stop down past f8.

Besides that, they have so much depth of field that you rarely need to stop down past f8 anyway.

The f/2.7 - 3.5 means the maximum aperture for the wide end and the telephoto respectively. The minimum will be somewhere like f/8 or there abouts. Possibly f/16.

The thing about small sensor cameras and their wide angle lenses is the DOF is pretty deep no matter where you set the aperture. Unless you're using the macro mode, you are going to have more DOF than you want in some circumstances. It is almost impossible to get a portrait with the background sufficiently out of focus.