I have read about the BitCoin project in early 2010 and it seemed like a booming project at the time, a time when its value was about $1.
Looking at the charts from MtGox.com over the time, there was a huge jump in BTC value in April. I speculate it's due to the sudden demand for anonymous money transfers to support LulzSec and other Hacktivism groups out there targeting Sony, other organizations and governments.
Not just that. There has been a lot of media attention for Bitcoin, not just regarding Lulzsec etc, but most importantly things like Silk Road.
While I noticed a huge rise towards $33 then a major drop to $10, the market recovered within 8 hours to $19. I haven't seen any stock exchange system ever recover in this speed before! And if you're wondering, that huge drop was due to LulzSec withdrawing 17,000 BTCs.
Lulzsec never claimed to have been responsible for that transaction. They simply tweeted the link.
Yesterday MtGox was under another DDoS attack and the traded volume dropped from ~47000 to 33000 and now it's 29000 (27500 when I finished typing this post).
The daily variations in BTC value is what attracted me to the BTC market, to trade. I've invested about $900, rather than buying gaming graphics cards and mining which would cost much more than $900 and the return value is quite minimum.
After much reading, I still do not understand what gives BTC its value. If it's demand, then it's currently powered by Hacktivists out there and if they cease their operations, BTC will drop back to its value prior to April: $6, if not less.
Bitcoin is definitely not just fueled by "hacktivists" (also, Lulzsec are not hacktivists, they are quite literally doing it "for the lulz").
Moreover, what if these Hackivists decide to DDoS major mining projects? The amount of generated hashes/blocks a day will greatly reduce causing the difficulty factor to drop, which means faster BTC generation (for the mining sites that aren't being DDoSed) which means more wealth when the DDoS attack stops and the difficulty increases again.
While I doubt Lulzsec, Anonymous, etc. would DDoS mining projects, exchanges, and other Bitcoin-related sites, the concern is reasonable. That is why it would be better if there were a lot more smaller pools and exchanges, so that one hit cannot have so much influence on the entire economy. If someone really DDoSed the major mining pools for weeks on end, and these pools would not be able to get back up, it could indeed be an issue.
EDIT: Whoops, almost forgot. The value of BTC is based on supply and demand - and indirectly on what people think the value is. Just like gold, and fiat currencies, if noone sees value in Bitcoins, they wouldn't have value. However, I believe that because Bitcoin is technically sound and has certain advantages, that alone is enough reason for there to be a value for at least a small group of people.