It's easy to quote a reasonable Bitcoin price at any given time, but determining the true value of the cryptocurrency can be an entirely different task. When people ask me what the Bitcoin price is, I just look up the rate published by an exchange like Bitstamp or Coinbase and round to a nice even number. For instance, today, I'd probably say that a Bitcoin is worth about $250. I also like to use BitcoinAverage from time to time, because the service creates an index based on the trade volume at different major exchanges.
Bitcoin Prices at Exchanges
The small price differences between the exchanges are interesting to note but not especially confusing or problematic. The only time when there was a gigantic price spread for a prolonged period of time was when MtGox was going underwater. The exchange was refusing to let users withdraw fiat currency, so nobody wanted to sell Bitcoins there. Instead, everyone at MtGox was buying Bitcoins so they could withdraw them - which drove the Gox price sky high. For several weeks, it was around $100 higher than all the other exchanges.
In normal times, however, the price differences between exchanges are usually only a few dollars and it's easy to understand why they occur. Not every exchange is identical. They don't include the same order books and the same traders. Some people might prefer to use a certain exchange because it has lower fees or for legal or geographical reasons.
Some people do use multiple exchanges, however, and those people help stabilize the price through a process called arbitrage. It's quite simple, really: They buy low and sell high. When two exchanges have different prices, traders with access to both of them can sell Bitcoins for the higher price and immediately rebuy them for the lower price. If everything goes smoothly, that's instant profit and the gap between the two prices will begin to close.
Arbitrage is not for everyone though. It can be hard to profit from it because both exchanges will charge fees for your trades, meaning that the price difference has to be enough to cover those costs. In addition, because the prices are usually only slightly different, it takes a lot of trade volume to begin racking up any real profit.
Bitcoin Prices Over-the-Counter
We've still only considered minor price differences, however. In reality, prices outside of the exchanges can easily vary by several percentage points. It's not uncommon to see 10% markups or 5% discounts when people trade with alternative methods like Paypal, bank deposits, or physical cash. Those discrepancies can have various causes.
In some cases, a Bitcoin buyer might be willing to pay more because he does not have access to an exchange in his country. Perhaps he only has access to a service like Paypal. Bitcoin sellers are likely to charge extra in a situation like that because Paypal transactions are easily reversed (and are therefore, very risky for sellers to accept).
Another important factor is anonymity. Most exchanges require users to submit a plethora of identification documents. Occasionally, they will allow small trades with minimal identification, but any real trading will require a government-issued ID, a social security number, and maybe more. Some Bitcoin traders refuse to deal with that and will pay more for anonymity. They might sell their coin for a few percent below market price if a buyer is willing to pay with cash in the mail or in person.
More Bitcoin Price Factors
The discrepancies listed above are generally the only ones that matter for day-to-day trading, but when it comes to ultimately valuing Bitcoin, there are all kinds of new factors to consider. Everyone has different opinion about what the Bitcoin price should be now and what it might be in the future. Trying to predict prices is certainly fun but rarely accurate.
One interesting factor to think about is the cost of mining Bitcoin. This recent story explains that the fair price of Bitcoin might be around $518, based on the costs of mining hardware and electricity. In general, if miners are regularly losing money, then the market price of Bitcoin might be too low, because miners are paying more to obtain Bitcoins than they are really worth. Or if miners are regularly taking large profits, then Bitcoin might be overvalued.
When it comes down to it, there is really only one way to determine the best Bitcoin price (or anything's price, for that matter). Only you can value Bitcoin. If you have absolutely no desire to obtain or hold Bitcoin, then its value is zero to you. If you need Bitcoin badly and you're willing to buy it with Paypal, then the value of Bitcoin might be higher for you. Your buy and sell prices depend on your own situation, and every person's prices combined create that wonderful phenomena we call the market.