Pemberville Free Fair...duh
My favorite even that is still going strong is the Hartford Fair in Licking County. Technically an independent fair and not a count fair, it was absolutely the highlight of the year for me growing up. It was one of, if not the only, fairs in the state to have dorms for the kids that were showing animals or had any other projects displayed at the fair (the dorms have since been nixed). And by dorm, I mean a large barn with bunkbeds in it. Fun times were had. If you haven't been to the Hartford Fair and it's not a long drive for you I would highly recommend it.
My favorite event from my childhood that is no longer around, and hasn't been for some time (probably 20 years or so), was the Black Hand Gorge Festival. The podunk town I grew up in has a pretty sweet State Nature Preserve (Black Hand Gorge, duh) and we used to have a yearly festival in the summer to celebrate. We had a few hundred people that lived in the town, and the festival would bring in thousands of people and absolutely pack the place. I'd be curious to find out if there are historical attendance estimates because I'd be really curious to what the numbers actually were.
Anyway, there was a parade and each grade in our elementary school would build a float (that elementary has now consolidated with 3 others into one building, and the old building is now a church). People running for office would have a float or walk in the parade, a marching band would lead, etc. The school grounds were covered with vendor booths selling all sorts of stuff. I remember buying a ton of baseball cards from two specific booths, and I can still picture the way they were laid out, and where they were located on the property. Tons of antiques and lots of random junk. I'm sure I would appreciate it even more as an adult, so if you know of any events still going that sound similar please let me know.