How do you obtain bitcoins? This is a question many people ask when they're introduced to Bitcoin.

Bitcoin sounds interesting, but if I want to use this system I will need to get some coins, otherwise, there's no way I can spend them! How can I start?
Exchanges
You can use an online exchange such as BitStamp for US dollars, as well as many others for dollars, and other currencies.
See the wiki for a full list of ways to buy bitcoins.
Brokerage Services
Brokerage services allow you to buy or sell directly from them instead of relying on a third party to offer the trade with the exchange just taking a cut. One such service is Coinbase.
Local / In Person
You can use tools such as localbitcoins.com to find people near you who will trade cash for bitcoins. (Note, however, that localbitcoins strongly encourages you to use their service despite the fact bitcoin does not require using a 3rd party to do in person transactions)
IRC and Remote Trades
You can use bitcoin-otc's web of trust system to improve the likelihood of a successful long distance trade.  This could help you do trades with people you find on IRC channels or Bitcoin Forum.
Hardware Mining
Mining bitcoins is very technical, and not for many people.  Unless you already have the hardware and technical skill to set it up I would not recommend mining as a way to get bitcoins.
Accept Bitcoin
I believe by far the best way to get bitcoins is to provide goods and services for bitcoin.  This stimulates the bitcoin economy which in turn makes the bitcoins you receive more valuable.