When I was more young-and-foolish (nowadays I'm old-and-foolish) I did a little, mostly around the UK. Some favourites were:
What is now the site of Deepdale Retail Park in Preston was light industry (a brickworks, a Coca-Cola factory etc.) in the 1970s and then just became a... nothing... for until 1993. One of my earliest jaunts of urban exploration was a friend and I lifting a manhole cover to explore the tunnels and cellars that had once existed below the factories of the site.
Whittingham Hospital was large secure psychiatric unit in Lancashire until it shut down for good in the early 1990s. On a couple of occasions in my teens some friends and I would cycle out there and scale the fences to break in to the ruin. It was, incredibly, exactly as creepy as every horror film would make you
think exploring an abandoned mental ward (with a terrible history of abuse of patients by staff) was. Strangely, it always felt like it was abandoned in a hurry: we found filing cabinets full of typewritten files, left to rot in old brick buildings with broken doors and roofs. Years later - presumably sick of urban explorers breaking in! - the council made the fences more-secure, and a couple of decades later I gather than the site's been mostly-demolished. Still a real shaping experience for me.
The bunkers of Hitler's Atlantic Wall, Hauts-de-France region of France. While many significant WWII sites are rightfully museums, many are simply abandoned. There's a pillbox bunker just a quarter of an hour's cycle from where I live right now, for example, that was part of the 3rd defensive line (part of the network of "stop lines" that would theoretically have allowed the UK to keep fighting had Germany engaged Operation Sealion and invaded mainland Britain), that's since fallen into the River Windrush but can be explored when the water level is low so long as you don't mind getting wet and aren't claustrophobic! Anyway: I took the opportunity when I was in France once to explore some of the "other side" of these bunker lines. These huge, concrete monstrosities are too numerous and monstrous to demolish, too commonplace for every one to be a museum about itself, so mostly they're just a crumbling concrete shell of the Third Reich's gun emplacements, just an older version of what they were when they were overrun by the Allies. I met a homeless family living in one of them, but my French was too poor to engage in a proper conversation and mostly I just wanted to give them their privacy (it's bad enough having to live in a decrepit bunker without a tourist wandering around your home).
Alexandria Hall, Aberystwyth: the first halls of residence of the University of Aberystwyth to accept female students, in 1896, ninety years later it got shuttered and mothballed and stayed that way until it reopened in 2004. This gave me and others plenty of time to break in and explore. I enjoyed how large and sprawling it was; how cavernous and bare, but this didn't feel as special as some of the other expeditions because it had clearly been explored plenty before we got there!
I've also found my way into and around several urbex places as a result of hobbies like geocaching and geohashing. A particular favourite might have been when
my partner's brother and I explored some old foundries, now completely buried in dense forest, during a geocaching expedition (itself while on the way back from a cross-country adventure, but that's another story).
That's off the top of my head, and I'd better stop because I keep thinking about more: disused railway tunnels (including one that wasn't as abandoned as I first thought, leading me to have to stand hard against the wall to avoid a passing freight train!) were always a hit for my dad and I, once upon a time!
But in short: yeah, I guess I've dipped my toe into urban exploring. There are culverted rivers under Oxford I'd like to explore, someday, as well as an old service tunnel I've heard about that runs underneath a major motorway (!), which sounds pretty exciting. So maybe there's still more for me to see and do.