Indeed there is a way. When the image you want is onscreen simply tap the 'Print Screen' (PRN SCRN sometimes) button. Now open your photo editing program, click Edit, click Paste and you have the full screen visible. On some programs you can right click and paste the image, each has their own peculiarity. Now use your resizing or crop tool to remove the bits you do now want then save the image. If I am saving for wallpaper I always elect to save as bitmap (.bmp) because it is a higher quality image than using .jpg

There are free screen capture programs out there that will catch a specific frame but I find that is as easy as anything and I do not need to remember how to work another program.

If you are running Vista, you don't have to do "Print Screen". Type in "snipping tool" in your windows search bar at the bottom of your screen. You can cut any portion of your screen with this Tool and save it as a jpg.

Here is a link that might be useful: Snipping Tool

Thanks for both replies. I was aware that I could use a screen capture approach, but the pictures I want to capture are sometimes small in relation to the size of my screen, so I am concerned about them getting too grainy if I blow them up as wallpaper. Is there an alternative approach that actually allows me to find the file for the displayed image somewhere on my computer, so that I know I am getting the highest quality file available?

If you haven't tried the "Snipping Tool", give it a try. I have saved a lot of photos and other things with it and they turn out pretty good. It has a couple of other options to save such as .gif and .png. It's certainly better than the old print screen, because you can choose a specific area to capture, and you don't have to "paste" it into any other program to use it.

kudzu9, I just tried using "Snipping Tool" on Photobucket by pausing the flashplayer, then enlarging the portion I wanted to capture with the zoom feature in Firefox. It's under view and make sure the "zoom text only" is not checked. The photo turned out looking very good.

I love picnik, you can get a firefox add on for picnik so that you will have new right click context menu items for picnic including send image to picnik to edit, once there you can edit it in many ways and then save the pic to your pc as a .jpg. You can also just go to the picnik site.
but with the picnik add on anytime I am on a pic I like even a flash one I just right click on it and choose the item in my menu to edit pic in picnik and it opens a new firefox window with that pic in it and then I can use any of the many tools to edit it or simply choose to save it and it will save it as a .jpg
Picnik Firefox Extension

Here is a link that might be useful: picnik

oh I just learned something new, there is now an IE add-on too!
Picnik Internet Explorer Extension

there you can see the various picnik tools

Don't forget, the web designer is torn between quality and speed. Most will use as small a jpg as possible because computer users have been brain washed for speed. So if a page takes too long to load most of us click away to a faster site.

This is exactly why I suggested saving as bitmap rather than jpg, so you do get something better.

Another thought you could try is to use Irfanview or your favourite editor increase the DPI (dots per inch) or resolution to improve the looks when saving.

Thanks, everyone, for all the helpful input. And ravencajun, thanks particularly for the tip on the Firefox/IE Picnik add-on. I think that's about as good as it gets for my needs, and so simple.