Our bank is on a Jack Henry platform and we are looking for alternatives to the "Netteller" online banking application that JHA offers. Do any of you use other systems or have any recommendations?

It depends. There are many vendors and they differ in their strengths and weaknesses. As discussed in other threads, there are also some real advantages to being with your core provider for internet banking. Not the least of which are superior integration and regulation by the FFIEC. If Jack Henry's solution isn't meeting your needs, they may also have an alliance with an outside provider that they would be willing to bring in -- and possibly you could get lower pricing from them.

What are your high level requirements and why are you looking? (e.g. specific features, pricing, integration with branch, etc.)