I'm think about building website with some kind of classic template.
I could do this with jsp:import, but that would mean that i have to paste few lines (header part, with title of the page param, banner/menu part and footer part) in each page and I would have to override the "content" part, and I think this is not exactly the idea of so called "templating". I know that in JSF is something like ui:composition, and I'm looking for something like this, but using JSP and servlets. Is there any jstl tag to do this, or maybe I should use framework like spring or struts?
That depends upon whether you consider 3rd party implementations such as SiteMesh or Tiles to be "frameworks".
If you want to roll your own, surely you can do that. Custom tags can be of great help here. Personally, I only "reinvent the wheel" when I feel that none of the existing wheels are acceptable. I'd suggest looking at the existing systems and evaluating them for your use before dismissing them out of hand and setting out on your own.