@HungryGuy and everybody else:
You can’t generate Bitcoins on a whim because generating Bitcoins involves solving a cryptographically hard problem: finding a chunk of data to tack onto a block which will make the hash of that block less than a certain target number (which is determined by how fast people have been solving blocks). That target number is lowered when the speed is too high and raised when the speed is too low. Since cryptographic hashes are for all practical purposes random with regards to its input, then your probability of finding a solution first is based on the ratio of your CPU speed to the total CPU speed of the network. Furthermore, the probability of solving it in a given guess is reduced for everyone when the target number is lower making it slower.
Now, for blocks, blocks are nothing more than a big list of Bitcoin transactions that other people want to be verified. A bitcoin node that is mining will take a set of Bitcoin transactions waiting to be verified and try to compute that number that makes the hash satisfy the criteria I mentioned in the previous paragraph. Once this happens then the node submits the block, signed with it’s private key, to the p2p network where it, and all the transactions inside it, is verified on a bunch of nodes.
In addition to the mined money that the person receives by solving a block, they also get all the transaction fees that people attach to their transactions. These fees will eventually be worth more then what you get from just mining, because there is an algorithm that determines how much you get for solving a block. “The coin value is 50 bc per block for the first 210,000 blocks, 25 bc for the next 210,000 blocks, then 12.5 bc, 6.25 bc and so on.” The limit as this goes to infinity will be the 21,000,000 bc, it will never actually reach that limit. BTW, attaching transaction fees to your transactions make including your transaction in a block more valuable so nodes will include it in favor of blocks with lower transaction fees because they get them as a reward for solving a block with your transaction in it.
The value of bc is no different than that of money produced by pretty much any government. Its value is determined by the market. Nothing more, nothing less.
I hope this helps solve you guys’ questions and concerns. Please read their FAQ: http://www.bitcoin.org/faq