I'm currently using dhtmlxGrid and we have the Excel copy/paste functionality working. dhtmlXGrid is the most full featured javascript grid package that I've found.
On their website, dhtmlXGrid claims to support Clipboard functionality in the Professional version. (However, I noticed the Sample on their site isn't working on my Firefox. EDIT: It's probably the permissions issue that Nathan mentioned.)
In any case, we had to do some extra work to get the exact Excel copy and paste functionality we wanted. We essentially had to override some of their functionality to get the desired behavior. Their support was pretty good in helping us come up with a solution.
So to answer your question, you should be able to get them to support copy and paste if you purchase the Professional version. I'm just warning you that it may take some additional work to fine tune that behavior.
Overall, I'm happy with dhtmlXGrid. We use a lot of their features. Their support is pretty good. They usually take one day to respond since they are in Europe (I think). And Javascript is by its very nature open source so I can always dive in when I need to.