What factors affect the value of a Bitcoin? Obviously the number of existing Bitcoins affects the value, but what else?  What are some of the primary factors for a rise or fall in a Bitcoin's worth?
The price for a bitcoin, e.g. for trading with other currencies, derives as usual from the interaction of supply and demand.

The supply of bitcoins increases over time, as determined by the rules in the software which is run by the majority of miners, and increases regularly over time, in decreasing increments.  It can also decrease when people lose access to the private keys which are needed to spend bitcoins.

The demand is driven by a variety of factors:


Bitcoin's utility as a flexible medium of exchange, with low transaction costs, efficient micropayments, little effective regulation, ease of becoming a merchant, pseudonymous accounts, and a worldwide market.
Impediments to the bitcoin economy caused by the friction and inconvenience of using bitcoins due to idiosyncratic software, difficulties obtaining bitcoins, relative lack of people who have bitcoins to spend, the risks of a new experimental currency, lack of understanding, etc.
Demand from new users, derived from recent publicity or new uses.
Speculation as to the future of bitcoins as an investment, over the long-term as well as the short term
Competition from related transactional or investment options such as Paypal, gold, etc.


Update Note that as long at the overall exchange market is relatively small, the market price can be manipulated by sufficiently well-funded investors who can expand the supply of available bitcoins, or increase demand, to meet their own goals.

See also the question and answers at What economics/finance methods and tools can be used to analyze and predict the Bitcoin market?.  (Previously I linked to this, which is now deleted:
What technical indicators might be appropriate for analyzing Bitcoin currency trading? - Personal Finance and Money - Stack Exchange)