I might help here too since I've owned - almost - all three cameras you mention...I say almost, because I actually did not own the latest Powershot SD870 (aka Ixus 860IS in Oz), but rather the 6 megapixel Ixus640 that was just before. Nevertheless, I can tell you about my experience with the Canon Powershot Sd-series, as well as the Panasonic TZ3 (which I did own) and the Powershot G9 (which I do own now...don't ask...).
* The Powershot SD-series
. Fantastic little camera. Canon image quality, sharp, well-exposed images, always. I believe that most (I'm not 100% sure on this) point & shoot cameras do not feature optical zooming, but rather digital zooming. I believe that the reason stated is that the noise from the motor driving the optical zoom would interfere with the sound being recorded. Thus, digital zooming...
However, I find that digital zooming when shooting movies in kind o
f alright, but in context of what you actually expect, I believe that you will not be satisfied with it (digital zooming). I think you probably want what digital video recorders do - that kind of zooming and quality - and you won't find that in digital point & shoot cameras.
Main advantage of the Canon SD870IS, compared to the other two you're looking at, would be its size. It's small, and probably the only one I would qualify as "pocketable". The TZ3 and the G9 are a bit bigger - not by that much -but nevertheless bigger enough so that they're in a size-class above.
* Panasonic TZ3
: Great build quality, and obviously its main advantage is the 10x zoom. One other thing I liked about it is the 30sec night shooting option, if you want to take longer exposures at night. Both Canon models are limited at 15 sec, although I found that sufficient for most night shots. Another big advantage of the TZ3 - and I believe the SD as well, although I'm not 100% either on this one - is that it has a wide-angle zoom. So not only it's a 10x zoom, but it's also wide-angle. I found that a really, really useful feature - a feature that is actually missing on the G9 (as I said, not sure about the SD870IS).
* Powershot G9
: This is what I own now. Its main advantage is that it's almost like a mini-SLR control-wise. Of course, I'm not talking about high-ISO noise capability here (more on that later) or lens inter-changeability (although you do have some options that the other two don't. See http://www.lensmateonline.com/newsite/G7.html
). With the G9 you can control shutter priority, aperture priority and manual control, and control over the ISO in a very, very intuitive manner, in my opinion. This gives you creative control that the other two cameras can't even touch. It's also the best built one - built like a tank. However, it does not have the zoom-reach, nor the wide-angle, of the TZ3. It's also the heaviest, but I kinda like that, feels like you're getting your money's worth, especially since it's also the most $$!
* All three cameras will give you great shots. All three have Image Stabilisation, and all three have a nice 3" screen.
* The SD is the smallest, the TZ3 has got the zoom and wide-angle, and the G9 has got the control features.
* All three cameras will give you - for all intents and purposes -the same graininess of pictures at high ISO. The thing with the G9 is that you can control that, so that it won't go above a certain ISO (say,200 ISO), whereas the other two will just choose whatever is necessary (i.e. 80 ISO)
to expose correctly (but with graininess, aka noise).
* The only reason I would get the TZ3 is if wide-angle and 10x zoom would be paramount to me.
* The easiest to operate and carry around is the SD-series.
* The most complete is the G9. I figure that if I'm going to have a point-and shoot of that "bigger" size, then I might as well have the G9 over the TZ3 - unless, as I said, the TZ3's wide-angle and 10x zoom are important to you.
* Think carefully about the size. Imagine yourself on holiday, and think whether you might leave the TZ3 or G9 at home because you couldn't be bothered carrying a camera in your hand, when you'd rather have one in your pocket. I know that many times I felt like that on holiday, when I wanted to sigh-see absolutely unencumbered - less to have stolen, less to loose - and when my little Canon SD was just perfect because it would fit in my pocket. Yes, you can carry the TZ3 or the G9 in your pocket - in the same way that you can
walk across fire if you really want - but I wouldn't. They are both cameras that, at best, live in a camera bag attached to your belt.
Please bear in mind that all I said is only my (opinionated) point of view. This is what I
would do, so - as Gordon said -you must decide what's best for you
Hope this helps a little!
after all my ranting, it occurred to me that, maybe, you want "apples" and we're selling you "oranges!" (I like my metaphors...). Have you thought that, instead of a camera that does average video, you actually want a digital video recorder
that does great video (and zoom!) and average pictures (some do have that capability, I believe. Up to a few Megapixels?...). Just a thought.