For me, the main value is that it is not centralized. No one can create more bitcoins than the original algorithm, no one can deny you using it, no one can “freeze” your account for anything and no one can take bitcoins from you legally (as on Cyprus).
The second thing that for me has value is it’s deflationary scheme. Every 10 minutes a new block is found and a new coins are released on the market, but that number of coins is halved every 4 years. Right now it is 25, on Nov, 2012 it was 50, and on about 4 years it will be 12.5. At this rate for 2030 the all the payments will be below 1 bitcoin per block and once we get to 0.00000001 the next halving will be below the max number of decimal points, so there will be about 21 million of bitcoins and no more never.
That is very good news for savers, because or money will be safe (if we keep our wallets in a secure, redundant place) and will gain value with time; with fiat currencies (dollar, euro, yen…) your savings are almost always prey of inflation…
A third thing is that bitcoin can’t be falsified. Can’t be double spending, like on fiat currencies, where one can create false dollars and spend them. That simply is not possible with bitcoin. This is also true with gold and silver, but it is very complex for a normal person to be able to differentiate a real gold coin than a coin of pyrite With bitcoin you only need to have the original software installed and you are pretty sure that all the coins sent and received are original.