Let me answer 'programming in general' as you did not specifically mention any language.
I happened to have majority of my experience in Financial Domain.
In general, I dont think you need to have any specific technological skills required unless you want to be in a very specialized area. Some Queuing /Optimization concepts, Quantitative Analysis skills etc are desirable in some but not all cases.
One thing I have seen is Financial domain is where poor DDD (Anemic) is widely popular. There will be use of wide range of design patterns in most of their applications.
Desktop based trading systems (Winforms like) are a bit more common in place here along with Web Apps. Remoting/WCF skills will be an added advantage. Database and SQl skills will required.
When it comes to functional knowledge, I never have difficuilty grasping Financial concepts. Only thing is it is vast, changing and can be easy to forget too. There will be Business Analysts to help developers, so not much of an issue. But it would be good to have some idea on basic Financial Instruments, Derivatives etc. (Use Investopedia).Generally, I find it much much easier than understanding Physics theories (where my background lies), where I want to move on with my programming.
And if you are highly skilled you can be a Quant, which is a tougher position and I don't have much ideas of it.