Can you please tell me how good the Fujifilm Finepix Z3 Digital Camera is? I am planning to buy one.Is it OK?

Here's a review of it on DPReview:

http://www.dpreview.com/reviews/specs/Fu...

-Karl

It's not a bad camera, it's small, light, rechargable, periscope zoom.

It's OK.
But there are better sub-compacts out there.
Check out the new Sony T100 for instance. A bit bigger- but they squeezed a 5x lens in a pretty small package- and it's not too bad at higher ISOs either. of course- it is a bit pricey.