You've undoubtedly received enough idiotic phishing mails designed to try and steal account details for banks you don't have accounts with to realise that malware developers are quite happy to develop very specific attack systems. However, the latest generation of banking-focused trojans combine this approach with a wide range of target banks, modifying their behaviour based on whatever sites you might visit.
At a briefing on financial security systems I attended earlier this week, Andreas Baumhof, chief technology officer for local security software systems developer TrustDefender, explained how versatile modern trojans are. It's rather disturbing stuff to add to our growing list of weird security attacks:
The trojan set is not defined these days by its mere existence. The trojan set is defined by what it does in a very particular situation. One trojan will behave very differently if you are in a confirmation page for Bank A to if you are on a login page for Bank B or if you are connecting with an application for a new loan at Bank C. It's not just question of detecting whether there is a trojan; you need to know with these sophisticated trojans what they do in particular situations.
As ever, the best way to running into these avoid these kinds of problems is to have a naturally cautious attitude and a multi-pronged approach to security, including protecting yourself from drive-by malware attacks, keeping your system patched and installing security software (there are plenty of good free options).