Saving RAW images

I went and took a few RAW images of the dog last night and the quality was night and day from the jpegs I usually shoot and this was only with changing the white balance. So once I open the RAW images in CS3 and make my adjustments what is the best way and format to save the adjusted image?

it depends on what you intend to do with the image
I often save in photoshop format if i have doen a lot of manipulation and layers etc.
also save as a TIFF
depends on how important the image is and how complicated the adjustment was

For final output, you are usually fine saving as .jpg. (use highest quality). Saves on disk space, and makes it easier to share your images with anyone.

After your initial conversion, you may consider making that your "master" copy (keeping the RAW as your "negative" too), and then only working on a second copy, that way you have an original to go back to.

If I have alot of edits, I'll save as .psd (photoshop format) so that I preserve my layers, and I could go back in and adjust them.

It really all depends on how concerened you are with preserving edits, and what steps you want to add to your workflow. (and everything etaf said too.)

I save the raw on the computer (in my lightroom library) and export to reasonable sized jpg (usually 80 to 90% quality) for web, small prints or slideshow viewings (e.g. on my projector).

If I've done PP in PS I save the PSD on the computer and when the folder reaches 4GB I burn it down to DVD and erase the files from the HD. That way I can easily bring back the file if I suddenly realize that I wanna try another edit. If the DVD should fail at some point I still have the jpg to look at and the raw/dng to work with.

Raw plus jpg are backed up on an external drive as well as burnt down on DVD.