I know at least all the Honda GX engines are still in production, which is what the harbor freight motors are copies of. The ubiquitous 6.5hp single that's found in everything from gokarts to cement mixers to snowblowers is a GX200 clone.
When I was looking for info about those engines(there's a surprising aftermarket and knowledge base for them, since they're used for kart racing), it's a pretty hotly debated issue among kart racers between the chinese motors and the Hondas. The copies are about 1/3 the price and a lot of people argue, since they are literally almost part-for-part identical, there's no real disadvantage.
Tecumpseh went bankrupt last year, and from what I'm hearing Briggs&Stratton isn't doing so hot either....these $100 HF motors are killing them....they can't even begin to compete with the price. The equivalent B&S motor costs $350-$500, depending if you want a stator, r/r, or electric start.
Quality wise I love the Series 1450 Briggs I got. Ball bearing crank, cast iron cylinder sleeve, reinforced case (it's a "red shroud", meaning commercial version). The "regular" black shrouds have bushing mounted cranks, are all aluminum, and don't have the extra ribs on the mounting plate. 10hp, 14.5 lbs of torque, electric start, regulated DC output. $900 retail....$120 because the UPS man dropped it and put a slight crack in the oil pan, which was fixed with jb weld in 30 seconds. Scoots my ass around at 50mph no problem.