As per the FAQ page:
Is there a limit to how many trading cards can drop?
Most games will drop a number of cards equal to about half of the number of cards in that game's set of cards. For example, Half-Life 2 has 8 cards in its set, you can receive 4 card drops by playing it. You'll need to collect the other half of the set from other community members. Try the beta group discussions, community market, barter with friends, and trade discussions. You can check how many drops you have remaining on your badges page.
In the instance that a game has an odd number of cards, for example Counter Strike: Global Offensive - which has a total of five cards - the number of cards that you can collect is rounded up. This means that you can get three out of the five cards.
The drop limit is permanent and it will not reset.
However, there now is an additional way of gaining cards:
Booster packs: Booster packs are additional cards for games that will drop periodically. Anyone who has collected all the trading card drops they can for a game and have used Steam in the last week may receive one of these booster packs. These packs contain three additional cards for the game, and may contain foils. If you receive a booster, you will get a "1 new item in your inventory" alert.
These booster packs are randomly given out whenever a badge is crafted (as can be seen by the badge eligibility text below).
As for statistics, there is now also a "How do I earn card drops?" link on the badge progress:
This then shows an overlay with additional information (what earned you card drops, in particular):
No. If they allowed this, it would be abused by people with multiple accounts.
For this same reason, you cannot get cards for free-to-play games without purchasing something first:
What about free to play games like Team Fortress 2 or Dota 2?
Free to play games drop game cards based on your in-game purchasing. For every $9 USD spent (approximate) since the start of the Steam Trading Card Beta, you will earn one card drop.
Best Answer
In Steam, simply click on your name on the top bar and then click on Badges - badges you have completed will be shown at the top of the list with a "Ready" button next to it. If you have not yet completed the requirements for the badge (ie: only have X out of Y cards), this will be stated next to the badge instead of showing the "Ready" button as follows;
This is what a completed badge with all collected cards looks like, before crafting the badge (and thus using up the cards), complete with a "Ready" button;
For a more detailed breakdown of the cards you're missing to create the badge, simply click on the game in question (for example, Left 4 Dead 2 in my screenshot above) and this will take you to a screen showing all of the cards required for a badge along with the ones you're missing, and information detailing things like which of your friends have certain cards, along with links to the Steam marketplace for quick acquisition.