After our Rescue course scenarios our instructor pointed out 2 divers getting ready--he said "See those two--They're doing a very thorough buddy check, indicating they just completed OW class and are very green. Keep an eye on them." That's the only time anywhere in my 5 years I've seen a "by the book" buddy check.
Must have been me! Snagged! Now everyone knows how green I am!

A SADDDDD ... (dive plan)
Sequence
Air
Depth
Duration
Direction
Distance
Deco
... will SAVE your life (in-water checks).
S-drill
Air/bubble check
Valve drill
Equipment check
When doing a quick check for a shore dive, I'll use a modified S-drill and make sure back-up and primary regs are working, do a bubble check, do a modified valve drill and just make sure that any potential equipment problems such as forgotten specialty gear is accounted for and drysuit hoses are hooked and working.
From a boat, we'll do a modified S-drill, valve drill, and equipment check on board then a bubble check during the descent and test back-up regulators again in the water somewhere at the beginning of the dive. This may be during descent or once we've reached a wreck.
When I do a serious dive, I check everything if I'm leading.
If I do a solo cave dive, I double check and take my time making sure that things are working just right. I use my mask as mirror to bubble check my manifold, regs, wing and tanks behind my head.