I have an FZ1v2... but I've researched the FZ10. I understand the FZ20 is an upgrade from that.
From what I've gathered (mostly from dpreview.com-->forums-->panasonic talk) the FZ10 (and 20) are very VERY nice. The "downside" is that they are geared toward real photographers, have lots of manual controls, and takes some practice and commitment to get the most out of it.
From what I read, it is a top-notch camera with quality lens, quality and more quality.
I am extremely pleased with my FZ1 and wouldn't hesitate for a second on the FZ20. I opted for the FZ1 over the FZ10 solely because of price. (There was a posting a week or two ago in HotDeals for the FZ1 at around $180) The FZ1 has a few less manual controls than the FZ10 or FZ20, but still has enough to keep me busy for a long time. I love this camera!
The image stabilization is an absolute must. Low-light is not very good on the FZ1 -- so if that's important to you, try finding real reviews concerning low-light pics on the FZ20.
Bottom line: Panasonic/lumix has an excellent product line. For a serious camera, the FZ20 would be way up on the list of cams to consider. For a quick snap-shot here and there, the FZ20 is probably way overkill.
edit: jeez... I just read that it comes with a 16MB card... you'll be lucky to get 8 pics to fit on that.
Factor in a new 256mb or greater SD card. Luckily prices on these are dropping like a rock.