I've aborted two of my own dives in many years. Most recent was due to a failed HP hose. Funny thing was it was fine while gearing up and getting into the water, then in 5ft just after submerging it started to 'fizz'. Had my buddy check what was fizzing, verified HP hose. Since no replacement in my truck, we called the dive. This was on my Prism 1, and the diluent cylinder is small enough I'm not taking chances.
An earlier failure was a scrubber bucket o-ring leak that wasn't evident on the pre-dive check, but started to bubble after submerging. Again, buddy verified bubbles and we both bailed the dive, went home, fixed the problem and carried on the next day.
I've also been on dives that were aborted due to gear issues with others on the team. Stuff does happen, and you have to adapt as appropriate.
I have so far only aborted one dive on the beach before getting wet. It was dive 2 of a drysuit course and the weather turned extremely nasty during the surface interval. What with super low tide on an crappy entrance and the very high winds, I just called dive 2. We regrouped and did the dive the next day at a much better site.
I can't recall truly aborting a dive once started otherwise. Low viz is a fact of life here. I will adjust dive sites based on weather reports or recent storms (often affect viz) but otherwise I'm gonna get wet.
In really poor viz I will call a dive early (less than 60min) but only in really, really horrid viz (< 1ft).