Currently (2013-04-01) the list of Leagues is:
- Bronze League: 8% of all players
- Silver League: 20% of all players
- Gold League: 32% of all players
- Platinum League: 20% of all players
- Diamond League: 18% of all players.
- Master League: The best 2% of all players. It is impossible to qualify directly into this League.
- Grand Master: The top 200 players in a region. Is created only after 2 weeks into a new season. Players that are not active for a certain time get demoted to Master.
Before you are placed in a League, you must play 5 Placement Matches against random opponents. After that, the game tracks your skill by assigning you a matchmaking rating (MMR), which is not exactly your League points, but similar. Different Leagues correspond to different MMR ranges, and it is possible to be promoted or demoted, if your MMR stabilizes within another League's range.
After a Season ends, all Leagues are wiped, but MMR does not. To be placed in a new Season, you have to play one Placement Match, which does not actually mean more than any other match - it is just there to filter inactive players from League rankings. Skipping several Seasons does reset your MMR.
Since some patch there is also a button to Leave League - if you feel that your MMR is well in another League (like if you are constantly encountering equal opponents from there), but a promotion just doesn't come, you can try to force it. Note that this doesn't reset your MMR, of course.
There is also a special, Practice League. When you start playing on a new account, you are placed here, and can play fifty games here before your placement matches into "real" Leagues (you can leave whenever you want though). Practive League matches are played on a special, more "noob-friendly" maps, that have destructible obstacles completely blocking bases off, eliminating early pressure. After you leave Practice League, there is no way back ever.
Further reading: Starcraft Wikia
All your 1v1s count toward your rating, regardless of what race you used.
On the league boards it will show whatever is your most commonly used race (where random is considered its own race).
Best Answer
I suspect your premise about gaining more points for winning than losing is slightly off. Generally speaking, once your point level stabilizes due to finding your actual skill level, your points will remain the same relative to others playing the game if you don't get any better/worse.
However, the total number of points everyone has will trend upward due to the Bonus Pool. This does mean it rewards playing more often, but only to a certain extent in a certain time period (a few games per week, I suspect). Once you've exhausted your bonus pool, your ranking points will again more-or-less stabilize based on your skill.
One of the reasons this was done was to encourage people to actually play the game. Since everyone's points are constantly going up, you have to play to keep up with your peers. If this artificial inflation of points due to the bonus pool wasn't in place, the player at the very top would - in theory - not have much reason to play; he's the best and his points will stay the highest until someone usurps him. This way, he has to keep playing to maintain his status. As with any fair matchmaking system, the more people playing, the better, and I think Blizzard is trying to encourage more people to play.
However, none of this is cut and dry so there's no one reason for any of these decisions; likewise it's not at all obvious whether this system is superior to the traditional ranking system you mention.
That said, here are some good articles on the subject:
Note also that the points you see displayed and used for your ranking may be separate from the underlying statistic used for matching you up against other players. The two stats should converge on relatively the same thing, but the Bonus Pool adds the extra incentive to play more often.