I've learned that one of the easiest ways to get a lower credit card rate is...simply to ask for it! Just call your credit card provider (major ones like Visa or Mastercard) and say something along these lines:
Hi, I'm calling today because I've recently received a lower interest rate credit card offer from _________________ (name of Company.) I would like to stay with you, but I need my interest rate to be lowered, or else I'll have to take this other offer.
It's really that easy! Last week I tried this method firsthand and was told that I would definitely receive a lower rate. Now, this is taking into account that the credit card is in good standing, and some other factors such as not just paying the minimum amount due on the card every month.
It's worth it to give this method a try -- post a comment if you try and DO get a lower credit cards interest rate!