When you log into your ISP, the IP address is allocated by the ISPs server - dynamic addressing. The ID is logged with the corresponding IP address in the server log. Thus for most people using their own accounts, identification is possible. It's the server logs that are usually subpoenaed.
Logging on via ASDL, ie continuous open access via your ISP,
I think, results in your ID/machine having a specific unique IP address.
In the case of internet cafes it would be harder to identify the individual user. If it is a cash transaction to use the machine and no record is kept of the users identity, then you're anonymous.
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