I used to cut the excess for test strips but since I do a lot of lith now I don't even bother. 8x8 on 9.5x12 paper (my favorite size but for some reason not available in North America). I like having a border to handle the print.
This question is more about how you compose than how you print. I.e. when shooting Hasselblad, I find myself composing square, while on LF or 35mm I compose for that frame (which could be both 4x5 or 2x3, depending on the frame given).
So, while trying to envision the print (eh, big words, but you know what I mean. ) I don't have the paper relative size in mind, just the way it prints etc.
My standard printing is on paper 24x30 cm (9,5x12"); picture size: 6x6 = 21x21 cm (22x22 cm); 35mm = 16x24 cm; 4x5" =21x26 cm; 5x7" = 17,5x26 cm (8x10 contact printing). Some pictures should have a smaller size, but to make that point I print it smaller but I don't cut the paper; just cutting paper to make test strips.(Of course, some prints should be even bigger but perhaps that's for some special display like exhibitions and the like.)
Like Rachelle I like a border to handle the print, also good to have in case of mounting. I think it nice to have my prints the same size in boxes of the same size, also such prints seem to make an impression when showing it to other people!
Used to do a lot of cutting in order to save test strips, but got tired of it (perhaps due to better economy!).
Print 6 3/4 in square in portrait mode on 8X10 paper. Leaves lots of white space when images are in an album or portfolio and simple to mat in a 11 X14 frame with a quarter inch of the paper showing under the mat. Think that leaving more at the bottom for signature might not be a bad idea instead of signing the mat. Even printing from a 4X5 I have been leaving a generous border and still printing full frame.
If I wanted to cover the entire area of the photographic paper I would most likely shoot 35mm, my 4X5 or a 645 but I really like the square format best but not exclusively.
The big thing about 6x6 is that you never need to turn the camera on its side, so no need for a prism. I've tended to find this quite liberating as I can shoot what I see and worry about the end result later as the least expensive part of the process will be the film. The tyranny of paper sizes is artificial so just crop the shot as you see fit and regardless of fixed paper sizes.
If I print square I center the image on the paper and have uneven borders which get trimmed off when I mount the print. Trimming the paper for test strips is a good idea which I had never thought of. Also my occasional square print could come from a 35mm, 6x6, or 4x5 neg.
I print all negatives to a size that best suits the final print. The image on a 6x7 negative may look best as a square print (say, 8x8-inches), and the image on a 6x6 negative may look best as a 8x10 print, or maybe 6x10 print. Generally, most of my images print best in a rectangular format, but it just depends on the image.
I voted for the first choice, as it is my usual practice when shooting my Rollei or Hasselblad. But I'm not anal about it. If I am shooting a TLR and see a scene that calls for a rectangular composition, I have no qualms about shooting it and later cropping on the easel. It is, after all, MY picture!
I've no doubt that the film format has at least some influence on what I see, so statistically I'm sure that I end up with a few more square images when I'm shooting square format than when I'm shooting a more rectangular format.
It also isn't unusual for me to print to a size that is customized to the image - not square, and not an 8x10 ratio.
Generally, however, if the image will end up square, I trim before printing, and use the scraps for tests.