The first two MLB games I went to were the Expos vs. the Giants, and the Padres vs. the Giants. In Arizona I also saw a few spring training games in Scottsdale (until their ticket prices exploded to four times more expensive than every other game at Spring Training) and quite a few regular season games when they came to play the Diamondbacks at Chase Field.
Oddly, the Giants fans I would witness at games in Arizona were pretty terrible. I haven't seen any other fans of MLB teams have to get kicked out of a game because of their conduct and that would seem to happen at every game at Chase Field. I would seem they were college aged guys acting rowdy and starting fights in the stands, or taunting the flag women.
The team does not seem to take on this unruly persona that travels with some of their fans. They have been a team more centered around laid back players like former starter Tim Lincecum and current ace Madison Bumgarner, who is so relaxed about baseball that he nearly retired not long ago just because he wasn't having fun with it. That fun seems to have come back as he has also embraced hitting as a pitcher as he has 14 homers, almost all of them have been in the last three years since the stories of his near retirement.
I used to live in New Britain, CT and would go to many AA games for the Twins affiliate at the time. They played the Giants affiliate quite a bit, who were located in the state as well. Bumgarner was a player whose AA debut was advertised on the radio and I had the chance to see him pitch for his first start above A. It was a packed night game and he looked like a literal giant among the other minor leagers. Even then, he had a smooth delivery and his wind up and physique reminded me right away of Jon Lester and Andy Pettitte. It didn't take him long to move his way up to the majors and he made his debut at the end of that season.
Another future Giant that I got to see play against the Rock Cats was Pablo Sandoval, except there wasn't the same fanfare for him. They used to have 10am Wednesday games in New Britain and I was working nights and weekends so the 10am weekday starts were pretty nice. They never seemed to get more than 20 people going to those games although sometimes there would be a small school or camp group. Because no one was going to these games you could sit where ever you wanted so my friend Brendan and I would often sit right by the on deck circle to get a good view.
At one of these games the Giants affiliate had a new catcher whose batting average was incredibly low due to his recent promotion who seemed to be looking around the stadium very aloofly, not paying as much attention to the game. There was something strange about him. He seemed to have his head in the clouds but he didn't seem bored or incapable of playing the game. In fact, he put a real charge into the ball when he made contact in a way that the other players didn't seem to be able to do. He was a bit of an anomaly and we had no idea who he was. We only remembered his name from the scoreboard because Brendan made note of it due to his oddness. Again, by the end of the year he was on the Giants and eventually Pablo Sandoval, too, was a World Series hero for the Giants.
The Giants seem to always construct their team in a way that I can't put my finger on why they are successful. They seem to just have really good talent scouts that are great at picking out players who are winners. It seems like the people who watch their players every day get a sense of potential from players because I remember some Arizona Fall League games where minor league fans of the Giants would come and cheer for Joe Panik. It was odd because I think Brandon Crawford played on the same AFL team, I thought Crawford was a little better (mostly because his coach seemed to have the same idea and would play him more than Panik) and he has been more of an elite player at his position in the National League. They are similar to the Royals that they have a lot of lineup depth and value hustle and speed.
The biggest difference with the Giants and the rest of the league is that they have THE catcher in the majors. Buster Posey is a former Rookie of the Year, MVP and three time World Series Champion. The Giants have won those Championships all in even years, '10, '12 and '14 and it seems like they have set themselves up for another great postseason run as they have established themselves both at the top of the Wild Card and NL West as they bounce back and forth with the Dodgers in the standings. They went out and stabilized their rotation this year with Johnny Cueto and Jeff Samardzija to give them three aces along with Bumgarner. This just seems like it might be the kind of a team that might play spoiler to the Cubs in the NL, and any team that gets into the World Series this year could win it all.