As JustAnotherDiveBum knows, my gear is ancient and barely functioning... but I trust it more than rental gear.
I've had a first stage "blow out" on a 100 ft dive off Chumphon Pinnacle in Thailand. Never did get an assessment of what actually happened. Could have been a burst disc, but the DM didn't think so. I didn't get a chance to look at the reg since we swapped out and returned to the dive quickly.
Diving with that same operator, I was handed a BCD that was so ragged I had trouble finding the actual arm holes. Of course I refused that and asked for another.
I don't mind renting things like wetsuits, weight belts, masks, fins, BCDs and the like but I definitely prefer having my own regulator whenever possible.
When I travel overseas, I obsessively research the outfit I'm going with. Thailand, for instance. We have been setup for medical relief work last summer and this summer - both have not materialized (MD/daughter instead will be on USA Indian Reservation - they probably need her more than Thailand). But, I can tell you with who we will dive with when we go - a quality trustworthy place and we will even allow her to do our overnight arrangements - in Southwest Thailand it is "Gekko Divers". I have never met this "Gekko Diver" in person (communication by email), but just follow her posts on SB and listen to what other say about her. My point is, I don't just show up at a place and then find out what kinda of place it is - I start the relationship way earlier.
I did this at the Red Sea - everything was in good solid condition. Now, the next 10 times I was diving there over the next 3 years - I brought my own stuff. Not because anything was wrong with their stuff, but because I like my stuff.
And I did this last summer at Tatsukushi Japan. I took/paid for that extra bag of scuba stuff, but as always, I carried on my regulator, mask, and computers. This was a top quality place, but it was in Japan - and my 5'10" 210lbs was too big for their little wetsuits and BCDs.
Obviously, there may be a place that you all of a sudden find yourself at and want to dive. Well, I'm not shy about protecting myself and others and calling a dive - and I will always use my credit card that stands behind me as the customer.
When I say "top quality", this does not mean "most expensive" - but it does mean places that share my values and have integrity. Then you get the gear that they would trust to equip their own children in.
P.S. Instead of taking flashlights with me when traveling, I now take my dive-lights - this is especially nice that all my lights are now LED. So I have a number of divelights in my carryon and in my check-in luggage. And if the luggage doesn't make it in time - well, I have my reg, mask, computers, and lights - and hope the rental BCD will be great. However, I am not afraid to call a dive.