Why would anyone buy BTC using MtGox when the price is so much higher than other exchanges (e.g. CoinBase)? And why would anyone sell using MtGox if you have to wait an outrageous amount of time to withdraw the USD? In other words why is MtGox getting any business at all?
The sole and only reason to buy there, is because you already have fiat stuck there and you want to get it out ASAP.
About selling, if you are optimist you can say that some people value that the risk of Mt.Gox defaulting plus the time they have to wait without their money is less than the price difference with the other exchanges.
If you are pessimist, you could say instead that they are simply stupid and do random things without really thinking about it.
Still, since there's no reason at all to send fiat there to buy BTC, yes, I agree it makes no sense for Mt.Gox to be still in business.
I use MtGox because of liquidity but also because of daily range. I usually exchange USD into BTC somewhere else, then send to MtGox to trade, then send somewhere else to convert back to USD. If I were to cash in/out USD at MtGox it would take too long. If I traded elsewhere I would not get as many BTC per trade/trend. Sending BTC to/from MtGox usually happens in a reasonable amount of time.
For instance, on 18 Dec 2013, MtGox low to high range was 224. On the same day Bitstamp had a range of 208 and Btc-e was 211. And I've seen more extreme examples with Coinbase.com, Kraken, etc.
A good multiday example is the Low on 6 Dec to the High on 9 Dec: MtGox: 492 Btc-e: 416
The increased range helps me believe that if I happen to get into a good trend that I will get the most BTC for my USD at MtGox.
I use my technical indicators to buy the pullbacks and sell at profit targets. After a few trades I've made more BTC with better liquidity than I would elsewhere.
The trading tools at Mt.Gox are immature at best but liquidity and range are very enticing.
People use MtGox for liquidity and out of tradition. MtGox has a terrible web interface and has terrible performance under load. It is dangerous to use MtGox when the market has a sharp correction because you may have to wait minutes between clicks. The crash in April was due to MtGox lag under load. However, API users on MtGox have good performance even under load. MtGox is a good choice for API access because it offers liquidity without lag while web users end up making bad trades due to lag.
MtGox usually has higher BTC prices. The only exception I recall is when MtGox prices fell faster than other exchanges. The recent explanation is that higher MtGox prices reflect a higher cost of withdrawing USD; however, earlier this year other exchanges had greater difficulty with USD and MtGox prices were still higher then. Price differences don't matter as long a prices move by the same proportion across exchanges.
I don't trust MtGox since the April crash. I was happy to be using other exchanges in the recent BTC price corrections because I could trade instantly using a good web interface that shows price movement on the same page that orders are placed. I don't believe claims of DDoS attacks because it is clear that the interface design requires constant refreshes page switches to do basic trades. If I were an API user then I'd use MtGox again due to the greater liquidity.