Yep.  Of course, there are no actual "coins", that is just a term used to make it easier for the average person to talk about.  But what represents the value of transactions in the blockchain ("inputs" and "outputs") can be traced back from address to address all the way back to when it first came into existence with a miner.

Now multiple inputs get joined together into fewer (or more) outputs so you end up with quite a tree of connections after a while, but if you want to follow it from address to address the information is all there.  The blockchain is a record of every valid bitcoin transaction that has ever existed.

Everything involving your bank in traceable.

You could try.

There are plenty of people who buy MoneyPak with their bitcoins from the two services which offer it (FastCash4Btcoins and BTCPak.com), but with that comes the assurance from a reputable party that has traded hundreds of thousands of dollars worth of these things.  It is a different risk profile with an individual.  But who knows, with the exchange rate rally, someone might be wanting to cash out right nao and be willing to chance it.

About the only interaction a bank has with MoneyPak is being able to use it to load a prepaid debit card.   There are not any standing offers to sell bitcoins for MoneyPak that I'm aware of.

Well, they use the ACH network to transfer funds from your bank account.  This is the same method that PayPal supports (by linking your bank account), and Dwolla, Serve, etc. all use the same method.  You had said no ID, and a bank transfer implicitly has your ID (as the bank has your ID associated with your account.)

Dwolla is among the cheapest methods of moving funds from your bank account to an exchange.  The exchanges which accept Dwolla are Mt. Gox and Camp BX.  The cost is just $0.25 per transaction.   The drawback is that there is a 30-day probation period after your first funds are pulled into Dwolla before you can then transfer money to a Bitcoin exchange.

Another method is Coinbase.  They charge 1% and their exchange rate is close to Mt. Gox.  The problem is that they max out at $100 per transaction.  
 - http://www.CoinBase.com

For larger amounts, Bitcoins Direct, a "bulk" dealer, is inexpensive.  They have a minimum $1,000 per transaction limit though.  They also don't always have coins for sale.

BitMe allows cash deposit at a Chase bank location.  The problem is that the liquidity isn't always that great, and slippage can occur -- sometimes even for a few hundred dollar's worth.
 - http://www.BitMe.com

If you have or can get ING direct, then that method to BitFloor might work.  There is a history though following their security breach that you may wish to familiarize yourself with though before choosing this option.

So that leaves bank wire to an exchange (such as Mt. Gox).  Bank wires are a costly method for anything but larger transfers.

Now there may be somone local who is trying to sell.  Sometimes they are just looking to trade at the current exchange rate (no fees).
 - http://www.LocalBitcoins.com