Meriden covered the pre-Hinckley Triumphs, so I'll just add my $0.02 on the ownership experiences of the 4 triples I've owned.
I started with an '09 Sprint ST, my very first sport tourer, which got me hooked on the genre. I fell helmet over boots in love with the 1050cc, though the rest of the package showed that they were trying hard but hadn't quite gotten it all figured out yet. The panniers looked like an afterthought. The underseat exhaust made the seat shape awkward and roasted my nuts. Best triple burble ever though. The '11 Sprint GT I later acquired fixed just about all the common complains about the ST. Brakes and suspension were still spec'ed on price point, but otherwise it was the quintessential sport touring motorcycle.
I also had a '14 Speed Triple R, which was dripping with Brembo and Ohlins goodeness... plus PVM forged wheels. SuperDuke and TuonoV4 might have taken the King of Hooligan title away by then, but the Speedie was arguable the most refined bike of the bunch. "Refined" and "hooligan" together might sound oxymoronic, but that, to me, goes at the heart of Hinckley's strength - the ability to imbue a motorcycle with the intangible qualities of character, personality, historical reverence, and that certain je ne sais quoi that make a bike exude cachet coolness and user-friendliness all at once. Not to mention reliability that would make Kiichiro Toyota proud. In the end, the S3R was like the prettiest girlfriend that I loved being with but knew deep down just won't make a good wife. Had to let her go.
Then came the Trophy SE. Wow... what a nice Grand Tourer it was, and ultimately... what a crushing disappointment it was. With the TTSE, Triumph went after the RT and succeeded in a big way... except BMW - in typically BMW fashion - came out with a new RT refined to the nth degree just a year after Trophy SE's introduction. Triumph decided that they are too small a company to keep up with the arms race with the Bavarian R&D Spending Machine, and that they were better off concentrating on making 31 flavors of Bonnie ice cream. Can't say I fault them for that logic, but it resulted in not a single sport touring motorcycle in their current lineup... and me without any prospect of buying another Triumph Triple in the immediate future.
Still, I think a few small stumbles cannot take away the monumental achievement John Bloor and his team has accomplished in a few short decades since the rebirth of the Triumph marque. It amazes me just how much influence this little British motorcycle company has had on the pulse of the industry. All of the retro and heritage motorcycles today - including a whole gaggle under BMW's tent - owe their presence to this genre the Hinckley crew popularized. By the same token, it was Triumph that made the nakeds and streetfighters into what they are today... spawning both Japanese and Italian imitators of their famed triples.
Triumph today is a savvy and innovative company, and, yes, they know how to make a motorcycle as good as any.