Bruce,
There are a couple of things you need to look at. Do you want a point and shoot style camera? Fits into a pocket or vest fairly easily? Or do you want a camera body where you can put different lenses on (DSLR)?
I don't think you can go wrong with either Nikon or Canon. I tend to prefer Canon just because that is what I know better but both brands tend to have excellent options. I have seen some good reviews on Sony cameras as well but I have never used one, so can't really comment on them. I currently have a Panasonic that is okay but I think it is just because I have not figured it out quite well yet. It is not as easy for me to use as the Canons in the past have been.
Pros of the point and shoot style:
smaller, easy to use, you can get a kind of hybrid point and shoot style that has more zoom more often found in the DSLRs, still have great quality, less expensive than DSLR usually
Cons of point and shoot style:
If you like action shots, there is often a delay from when you push the take a picture button to when the picture is taken. Also, if you leave your camera on all of the time so that you don't have to turn it on and off to take a picture, it often puts itself to sleep causing a delay in being able to take a picture. The hybrid P&S style is a bit chunkier.
Pros of DSLR:
You can get a decent to good body and buy excellent glass. You can leave the camera on and it is always ready to take a picture. Action shots are instantaneous when you press the take a picture button. You can change out your lenses to fit the situation (of course you might begin thinking oh man I need another lens)
Cons of DSLR:
More expensive than most P&S, typically the kits that come with body and lenses, the lenses are "okay", bulkier if you are carrying it around on your neck while out in the field
So, I suppose start with how much do you want to spend and what will you be using it for? More action shots? Some of the hybrid cameras might be what you want...they are still a little slower to take pictures when you press the button but you can always take bursts of photos and you get more range than a traditional P&S. Are you using it more for wildlife that is mainly sitting still or moving slowly? Wanting to get more photos of hunting dogs/companions or family outings?
Whichever route you go, the odds are very good that video will be an option already added into the camera whether it is P&S, hybrid or DSLR.
If you provide a little more info on what you are wanting to do, we might be able to help steer you more than saying Nikon and/or Canon are the way to go.
Dani