18 feet for 8 minutes is my record for shortest dive ever. It was a dive where my buddy's computer failed, so we called the dive.
Another was 16 feet for 9 minutes collecting bags of sand for aquarium husbandry purposes. I may have another short dive this Saturday, setting float and scouting the viz and conditions for a wharf clean up event. Shouldn't last more than 5minutes, but I'll log it.
For me a loggable dive is any dive with a purpose, may that be a fun dive, working on skills etc. If I were to descend and find a problem immediately, my computer may read 1min or it may have not even registered. I wouldn't log that. If however I've committed to a dive, and later aborted or complete one, I'll log it. Use your best judgment is what I'm getting at.
Agencies on the other hand have a specific requirement for what counts as a dive (in essence, what you can log as a dive). This pertains more to class settings, the way I interpret it at least. Instructors can have the final say when reviewing your log book to see if you have the required amounts of dives to sign up for a class.
My NAUI Standards and Procedures Manual states a scuba dive is one that includes an entry and exit and lasts 20 minutes at a depth of at least 15ft.
It does however give exceptions in case water temp or conditions make this unsafe. Substituting extra skills and/or entries/exits will suffice. A specific example it gives is a 12minute dive (including entry and exit) followed by a separate 8minute underwater activity (also including a separate entry and exit). Also:
NAUI S&P page 2.7 (rev1-04):
A series of excursions in a course involving 80minutes of underwater activity on scuba would comprise four scuba dives.
So from my interpretations, what constitutes a loggable dive is really more for the terms of fulfilling the minimum standards of a scuba course. From my interpretations, personal dives can be logged at the divers discretion, but instructors can always contest since it's their class. So log what you think should count and let your instructor have a final say if you're logging for a class pre-requisite.