Would it not make sense in a culture such as the one that we play this game in for the money to have individual identification codes, similar to the serial numbers on modern day cash currency?
In our culture, the paper cash itself has specific serial numbers, but money in a bank account does not, so I will not be suprised to hear that it would not. From a rules standpoint, I see nothing that suggests that there would be individual serial numbers for each nuyen in the shadowrun world, but my reasoning is this: In a culture where we are now dealing with megapulses of information, then details such as this would be fairly easily handled with the concept of the credstick.
Even with a certified credstick, if a bank were to put say, 2000 on it, then it would seem that each one would almost have to have some serial number on it to make it transferable (and uncopyable<--I know, not really a word, but you get the idea), in which case, it would concieveably leave a form of electronic paper trail. Naturally, with a certified credstick, no name would necessarily have to be tied to that stick, but it would allow the money to be tracked.
In our culture, every electronic dollar (to those of you whose country does not use the dollar, I mean no offence) is backed up with real cash, which is in turn backed (theoretically) by gold. In the Shadowrun culture, there would have to be some way of limiting the amount of currency that exists, otherwise counterfeiting would be as simple as adding 0's to the ledgers.
Honestly, I am just interested in this as a thought experiment, but would love to hear some of your thoughts on the subject.

Serial numbers on paper currency were generally put there as a measure against counterfitting. They are on occation used to try locate money stolen from sources that track the serial numbers. However, inspite of what people that envision their every move is tracked by black helicopters, there is relatively little tracking done on the path of serial numbers.

Also your assumption of the existance of physical cash in one-to-one reserves to electronic balances is simply is not true. Never was, even when the equivalent to electronic balances were paper ledger tracked funds. Further, in the modern era, many countries have done away with most if not all gold reserves that were underlying their issued currency. Several countries around the world have sold off massive amounts of gold in the past 10 years.

So there really is no reason to have a serial number as we know it attached to each nuyen in a cred-stick, no more than there is to attach a serial number for each dollar, mark, yen, pound, penny, etc. within current currency that has a value of more than 1 of the given currency unit.

The credstick has built into it fraud protection, and the ability to even track the flow of money (subject to the Zurich Orbital's archive storage space).

Hey, there are black helicopters. The new, new twenties have RFIDs in them, and if you don't believe me, microwave one.

I don't care what they say...All my money's marked

I just lined my wallet with tinfoil.

Not that it matters. I'm too poor to be affected by those RFIDs.

Those aren't RFIDs. They simple metal strips that work against counterfeiters in two ways.

1) You have to get your hands on not only the proper texture paper, but also paper that has that metal in it. Think of it as a metallic watermark.
2) You can't "wash" bills of a lower denomination. "Washing" is where you take, say, a $1 bill and remove the ink from it (modern currency never fully dries). The counterfeiter can then print the high denomination pattern on this paper. It is a relatively easy/cheap way to get hold of the proper feel paper. With this metal strip in, and in different locations for different denominations, washing is detectable by a missing or misplaced metal strip (that is relatively easy to machine read).

EDIT: Er, ya. Microwaving them is like putting a spoon in the microwave. Duh.