BitCoins (BtC) are a weird form of currency. It does appeal to persons of a certain ideological bent, but it has some pretty poor properties for a medium of exchange (which is what a currency is fundamentally for. Beats bringing two cows and a goat to the hardware store when you want a table saw...)
Bitcoins are designed to exist as a relatively fixed quantity of currency, with 'new' bitcoins made available through computational 'mining' to discover additional coins. Each coin is a unique computed value. The computational effort to discover new bitcoins rises over time, to the point now that special programmable application specific integrated circuits (ASICs) capable of performing hundreds of billions of cryptographic hashes per second are used to 'mine' for bitcoins. Since the supply of bitcoins is bounded, fractional bitcoins exist, each linked to an original bitcoin, to facilitate exchanges of smaller sizes than a coin.
Bitcoins are not actually anonymous or untraceable. Each full coin is computationally unique, and can be validated through an exchange protocol. When a bitcoin is 'mined' and registered by the miner, it starts a new block chain that tracks the history of the coin. This is needed to validate a coin as being real. Software exists to walk back through a block chain to identify the 'history' of a coin. Th anonymity comes from the nature of the online bitcoin 'wallets', which are abstract numerical values with a cryptographic basis themselves.
Bitcoin 'tumblers' exist as an online financial service to obscure the history of a specific transaction. These services charge a commission in exchange for mixing together many bitcoin transactions and deposits so as to keep a party receiving a bitcoin payment from identifying the origin of the payment by examining the block chain history of the coin. The payee gets the bitcoin amount the payer sent via the tumbler (less the tumbler's commission) but not the bitcoins proper. (Well, unless the payer is responsible for most of the bitcoins moving through a tumber, as in a recent theft case. Overload the tumbler and the back tracing works pretty well...)
The biggest issue I have with bitcoins is the deflationary nature of the currency. With a relatively fixed supply of bitcoins, and increasing quantities of goods and services that can be purchased, the purchasing power of one bitcoin rises over time. (This is the bit that appeals to some folks) Since there are fractional bitcoins, this doesn't mean that the marketplace runs out of currency, of course. It does have an interesting implication for economics. Since the value of one bitcoin will likely rise over time, there is a disincentive to use it as a medium of exchange, and an incentive to hold onto the bitcoin proper. This also acts as a disincentive to use the bitcoin to invest, as the bitcoin itself may grow in value, perhaps giving a higher return than if used for a capital investment.
This may sound familiar. 'Liquidity crunch', anyone? Deflationary processes act asa strong brake on economic activity. Yeah, just like late 2008 and early 2009.
There are other problems with bitcoins, but most of them are shared with other forms of currency. (Theft, anonymity of transactions, etc.)