These days, I mostly use my two Canon DSLR cameras, but I actually made my entry into digital photography with a point&shoot Olympus, the Olympus C-2100. I later bought a second Olympus to have a camera that I could easily put into a pocket and take with me at all times.
While I no longer use these cameras for serious purposes, they still enabled to get me into this hobby, and as such they merit being shown and described.
The Olympus C-2100 Ultrazoom ("UZI") was my first digital camera. It is a 2 Megapixel "prosumer" digital camera with 10-times stabilized optical zoom (equivalent to 38-380mm on a traditional 35mm camera).
Accessories that I had included lots of AA-size NIHM rechargeable batteries, two battery chargers, an UV filter, a polarizer, a fairly standard tripod, and 128 MB and 64 MB SmartMedia cards, as well as an Olympus 8 MB card for camera-assisted panoramas.
When I bought it in 2001, most professional reviewers had rated the UZI to be one of the top performers in the 2 Megapixel "prosumer" class. It allows a wide range of control over the photographs taken, as well as taking great point-and-shoot photographs, therefore (at the time!) catering for both serious photography and quick snapshots. Also, 2 MP coupled to a quality lens seemed to be a sensible compromise between image quality and filesize, with photographs in medium to high quality weighing in at just under 0.5 MB each.
The downside to the camera is that it is not all that portable (won't fit in a pocket), draws quite a lot of current out of the batteries, only supports SmartMedia (which don't exist at any size larger than 128 MB) and can't really be used for enlargements larger than 8x11". It still took many nice pictures and preserved memories that would otherwise be forgotten.
While the camera was decent enough to start out with, noise was higher than I liked, and I had also outgrown what features it offered and liberties it afforded. Furthermore, the camera was increasingly plagued by reliability problems. It spent the last two monts of 2003 in the repair center, and the camera went through a total of three crucial repairs in its two and a half-year "active" life. The repair center was seemingly unable to fix the last problem - very visible color banding in gradients (ie. a blue sky or smooth surfaces). After less than 20,000 shutter actuations, it was time to retire it for good.

My Olympus C-220Back when my Olympus C-2100 (described above) was my main camera, it spent a couple of months going back and forth to the Belgian Olympus repair center. When I was preparing to travel to the US for a month in early 2004, I needed a cheap camera to fill the gap between the Olympus that wouldn't get back to me in time, and the first DSLR that I wanted to buy in the near future. I wanted something that was economical (read: cheap to buy) and would allow me to use my existing Olympus accessories.
The answer was a 2 Megapixel compact camera: the Olympus C-220. Being the most entry-level camera with optical zoom in the late-2003 Olympus line-up, it never was a performer in any sense of the word, but good enough for decent pictures in sunlight.
After I bought the Digital Rebel, it also served as a good alternative whenever the former was too precious or heavy to use - while hiking on a strenuous trail or while driving, for example. It keeps serving me for that very same purpose in 2006.