The first "real" dirt bikes that many of us old guys ever experienced were very far removed from what anyone could consider as a dirt bike today. Back before my time the Harley Sportsters and Triumph Trophys were considered dirt bikes except for a few English 350cc and 500cc singles.
For those of us who entered motorcycling in the mid-sixties the first dirt bike we were exposed to were the Honda CL72's and CL77's (or the Trail 90). The Honda 305 Scrambler was a high piped 350lb twin with a generous 3-1/2" of travel in the front fork. It won Baja, introduced thousands of us to off-road adventures, left burn scars on the inside of our left leg when it fell on us and made a glorious sound unlike any bike before or since. They were big, (relatively) fast and looked cool and it was my first motorcycle. It was true pig off road but when you're sixteen who cares - it was fun.
Yamaha changed the world when it introduced the DT-1 250cc in 1968. Sure there were other two stoke dirt bikes out there (who can forget Hodakas?) but the DT-1 was the first mass produced, relatively light motorcycle that was available in huge quantities to feed the growing off-road market. At one time almost half the guys I knew who had motorcycles owned a DT-1 (myself included). They didn't handle that well and you fell down a lot but they really dragged a lot of guys into the sport.
Then came "On Any Sunday" and Huskys became the thing to have - a friend of mine got a Husky 360 - he was the fastest guy in the pack without question. I bought an Ossa - it came equipped with knobbys and better suspension than the Yamaha and I stopped falling down so much. The dirt bike world exploded with new models coming out faster than you could keep track but I'd say those old 305 Hondas were the seed bike for a lot of us fifty-somethings.