The immediate example that came to mind, out of a huge amount of options over the years, is a connection in Newport off a train from Hereford onto the westbound morning FGW Pullman service to Swansea one time.
On this occasion, I'd been due to miss it by something like 65 or 73 minutes, I forget the exact number given this was more than 15 years ago. Some issues further east meant that I joined the HST with the Pullman service much to my delight
I'm sure there's been many times when a delay has worked in my favour, such as reducing a long wait to something much more tolerable or making a connection further up the line work out on a long journey, but to be honest I don't remember them all right now.
Wait, no, I do remember one other right now. Another one from years ago, when I used to live in rural Herefordshire. I'd arrived on the first bus of the day with a known lengthy wait of around 50 minutes due, onto the 0845 or whatever it was at the time to Birmingham New Street. Delays elsewhere meant that the 0709 was running something like 38 minutes late, so I got to the Midlands much earlier than expected and that pleased me hugely
Clearly the coffee's now kicking in, as I remember one from earlier this year. While in North Wales, I'd gone with my Blue Beauty and I was ticking off a 230 and a couple of stations as part of my adventure. Due to a rather significant misjudgement on direction, thrown off by an enormous overpass of the A55 causing me to think the other roundabout was the wrong one, I was a bit late getting to Flint. Fortunately, the 175 I was due to connect with was a good few minutes late itself

I'd known it was late, otherwise I'd have needed to go at a pro cyclist speed to make it, but the extra 3 minutes delay really benefitted me
