This post is part of my own experience as i too had a spare router :). If you too have one and dont want to throw it away, then read on. If you have a relatively big apartment, then the signal of your existing router may be dwindling at some places and internet may not be usable at such places. Since you have a spare router, you can configure it to act as a repeater, so as to improve your signal strength.
Most recent routers are capable of doing this. However if you purchased your router before 2007, you might need to do a firmware upgrade for your router. Detailed instructions on how to go about configuring your router to act as a repeater and also upgrading your firmware (if required) are available at the following link :
WRT wiki : This How-To provides step-by-step instructions for creating a Universal Wireless Repeater appliance: a device that you can place anywhere and it will wirelessly repeat the strongest signal, onto another wireless network (with or without security). This functionality is also known as Wireless Client Bridge, or Range Expander.
So go ahead and give it a try and make full use of the forgotten box 🙂 .