1) speculation
2) attractive store of value due to the deflationary nature (note that not all cryptocurrencies are deflationary)
3) True limited supply that's mathematically guaranteed. Gold supply, for instance, is not limited in any practical sense, there are trillions of tons of it in our Galaxy, it's all a matter of technological advanvements of its extraction.
4) secure transactions that can't be reversed (though you can use escrows if you want the reverse option)
5) low transaction fees (except for bitcoin)
6) inability of anyone to stop you from moving the money in your possession. See 'paypal sucks' stories, civil forfeiture.
7) works extremely well on the internet
8) fast transaction settlement
9) works over almost any protocol, you can technically manage bitcoins with a dumb phone over SMS
10) banking for those who doesn't have access to banking
11) libertarian aspect - no government control
The Bitcoin price is justified by the free market. People want it, they are willing to pay for it. That's true of any currency value, btw, since there are no government currencies pegged to gold, it's all based on whether people believe in the currency. When they stop believing, we get Zimbabwean dollar, Venezuelan Bolivar, USSR Ruble, Argentinian peso.