Yes you can.
3rd party wireless routers are widely available. The options open to you depend on your current internet connection.
Buy a cable router, you cannot replace your current router, you can only treat it as a modem as it has your internet connections settings hard coded into it and cannot be tranferred.
ADSL/BT phone line:-
You can buy a cable router and chain it with your existing router for a simple setup.
You can buy an ADSL router to replace your existing router. However, this does mean you need to setup your internet settings on the new router. This has the added complexity that settings vary from ISP to ISP and from package to package.