In the online identity world, the concepts of anonymity, pseudonymity and traceability all seem to be regularly confused with each other in one way or another. Whenever you here someone speak of anonymous transactions, they almost always bring up cash as an example of a real-world equivalent -- however cash isn't anonymous because you typically have to hand it to the relying party, thereby giving up some level of your anonymity.
So, I'd like to suggest we consider the following "definitions":
- Identified transactions - transactions that take place under a public identity of the user (such as when I use my credit card which has a unique serial number and my name printed on it). Most online transactions which involve the exchange of money fall into this category.
- pseudonymous transactions - transactions where the actual identity of the user is not provided to the relying party, but when the same user performs multiple transactions, the relying party can tie those transactions together under the same "pseudo" identity. Pseudonymous identity systems typically have requirements to protect against multiple relying parties from tying transactions together by using a different "pseudo" identity for the user at each relying party.
Traceable transactions - transactions where the user's identity is not provided, but there is some identifier included in the transaction such that if there was a need someone could eventually trace it back to the issuing party. Most real world transactions are at least traceable because they require that the person who wants to invoke the transaction (e.g. make a purchase) to interact with the relying party (the person at the cash register) and that interaction can lead to traceability (not to mention that the physical cash bills typically have unique serial numbers as well).
An example of an online equivalent is the user of one-time-use credit card numbers which would never be used again and so can't be used to tie transactions together, but can be traced back to the user through the credit card issuer, if necessary and authorized
anonymous transactions - transactions where the identity of the user is not known and the transaction cannot be tied back to the user in any way.
Access to most published/open web sites which don't require a login (such as google) would be considered anonymous (if you don't let them create cookies on your browser -- the cookies would make them pseudonymous).
Most cost based services (high value transactions) require some level of identification and thus are not processed in an anonymous fashion.
When you listen to some privacy advocates (and to some people with a product to sell), you would think that the world can't operate without things being "anonymous". I disagree and think that the real and online world has to operate across a spectrum of transactions that span the types above (and probably have some in-between combinations).
Ultimately, the real driver should be towards "just enough" and not towards "none". Ensure that transactions have enough information such that the transaction can be completed, but don't ask for or give any more than is necessary. That is one of Kim Cameron's Laws of Identity (and I think, perhaps, the most important.