Keyword rich URL – an SEO must-do or just an option?

I am curious, how big is the difference between keyword rich URL/URI and one made up from random sequence of characters, like product number/code. Does it matter enough, so we should consider switching over to a completely new URL structure, or it's just not worth the hassle?

Our site is 6 years old, and over the time, there are many articles (up to one thousand articles actually). Our main source of traffic is organic search traffic and I don't really want to screw that up. It took us 6 years and quiet a lot of money too.

Thanks guys.