I'm no expert, but I'll give a shot at a simpler response here.
I had been using a Canon A710IS which boasted a 6x zoom, but I too wanted more zoom. (Like cowbells, you always need more zoom...
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The zoom was listed as 5.8-34.8 (hence the 6x). Given the sensor size of 1/2.5" (5.75 x 4.31 mm, 0.24 cm²), this translates to 35-210mm equivalent for a 35mm film camera. (Ie, to compensate for smaller sensor, multiply focal length by a factor of 6. I think this is what others are calling the "crop factor.")
As I did my shopping, for example, I determined the following sorts of zoom range equivalences.
Panasonic FZ35 w/ 18x using a 1/2.33" sensor and a 4.8-86.4mm lens (use 5.6 factor to get 35mm equivalent) >> 27-486mm
I ended up with a Pentax K-x which has the APS-C sensor. (With a 1.5 factor for 35 mm equivalences)
Using the 18-55mm lens > 27-82.5mm
Using the 50-300mm lens > 75-450mm
I think this is a useful enough rough guide, and I do indeed have more zoom!