Auto 5*
*The Auto 5 is more mechanically reliable than any of the gas guns I've used. What it's not, however, is idiotproof. If the user sets it up improperly for the ammo being fired, it will jam. However, being recoil operated instead of gas, it doesn't fill up with fouling and jam.
However, you asked also for most popular in clay games and tournaments, hunting and home defense. The A5 is unlikely to win in any of these categories. It is, after all, 115 years old, and kind of odd. Clay shooters use lots of Berettas and Remington, depending on tax bracket. Berettas hold up better, Remingtons shoot softer. Three-gunners tend to favor Benellis and Remingtons, with similar reasons. Hunters use all kinds of crazy stuff. Lots of guys I know buy whatever had the snazziest ad in Field and Stream. Every year. HD is similar, except for choice of magazines.