I just got back into wrestling and I remember how back in the day a lot of my favorite wrestlers like Great Muta, Masahiro Chono, Jushin "Thunder" Liger and Ultimo Dragon used to wrestle there. I even heard that a lot of American wrestlers (even guys like Hogan) used to wrestler there.
Foreigners wrestling in Japan is one of the staples of puroresu. For decades, the "local guy vs gaijin (foreigner)" feud/match was what drew the most money in that country. It wasn't until the 80's were other forms of feuds and rivalries began to draw big as well. So yes, almost every big US star went to Japan because they were paid a lot of money to work fewer dates than in the states, be respected and protected. Guys like Lou Thesz and Karl Gotch were fundamental for wrestling in the Japan taking off and from then on, all the "names" made a trip to the island to make some good money.
Plus, I heard that pro wrestling in Japan is like football is in America and that their big show is like our Super Bowl over here is.
It's not nearly as popular as football is in the US. Baseball is Japan's n°1 sport, Sumo takes n°2 and Wrestlings is n° 3. Nowadays is a distant 3rd as most of the business is in the shytter, most companies barely make any money and are forced to do shows in small buildings except 1 or 2 times a year. New Japan and Dragon Gate are the exception. If you'd like to know why that happened I and other would be happy to explain it to you, but there's an official thread were more people could take notice of your questions.
New Japan's big event is the January 4th Tokyo Dome show and even though is by far the most important show of the year, it's not even close to a Super Bowl feel. You can say it's their Wrestlemania though. But honestly, every promotion has it's yearly "big Wrestlemania-like" show. When business was booming, they used big buildings like the Tokyo Dome (or other baseball stadiums) but now that hard times are upon them, they use smaller places like Sumo Hall (11,000 capacity).
So, has anybody from over here ever gotten an opportunity to watch the shows they put on and how are they?
How do they compare with WWE/WCW/ECW and American companies?
A lot of us watch/have watched puroresu. We have an official thread, there's some interesting stuff in there
http://www.thecoli.com/threads/japanese-wrestling-discussion-news.33877/
They are pretty different. Weekly TV shows are nothing alike US wrestling, you very rarely get an in ring segment or an important promo. Honestly, if a puroresu show makes air it's because it's either a house show to build up a big show, or a big show itself.
The first matches are normally filler or lower card feuds and the matches are treated as such - not a lot of time, not a lot of crowd heat, may have a few comedy spots to pop the fans - and almost never steal the show. But once you get to the top 3-4 matches, you'll get quality that you'll never get in the US (if you like japanese wrestling style, you gotta consider not everyone likes it).
Depending on the Era you are watching (80's, 90's, 00's, 10's) the quality of the show varies. Cards from the 90's are mostly outstanding with most companies having 1 or 2 great matches in all their big shows.
Do you think it could become popular here?
Nope. The language barrier will always be the downfall of puroresu in the US. As much as people who watch it rave about the in ring quality, the truth is the majority of the audience wont watch a show or spend money on a product solely based on in ring action.
Even New Japan, that lately has had more buzz than in the last 17-20 years, barely gets a couple of hundreds non-japanese buys for their iPPVs. They toured the US a couple of years ago and had mediocre gates at best. You put their product on US TV and no one but the most hardcore of hardcore fans will watch it, and that's not enough.