There are a lot of commercially designed K-cup holders that would work for getting them up off the counter and out of your way. Carousel holders are particularly popular. Not only do they look cute, but they make it easy to see all of the different flavors. The only downside is that they still take up quite a bit of space on the counter, which is not ideal if you have a small kitchen.
Another option is to get a small drawer that would fit under your coffee maker and store them in the drawer.  They make these drawers specifically for K-cups, but you could also check out drawers that are made for fishing tackle or for beads. Just be sure the height of the drawer is tall enough to easily accommodate the K-cups. The main benefit of this option is that it doesn't take up much more room on your counter than your coffee maker is already taking.
If you want to keep your K-cups out of sight, an over-the-door shoe organizer hung on the inside of your pantry door is the perfect solution.  Ideally, you should look for one with pockets that are made from clear vinyl so it is easy to see what flavor you are grabbing.
Finally, I really love this idea for a DIY K-cup holder that I found on YouTube. In it, she makes a K-cup holder out of a shoebox lid and a bunch of old toilet paper rolls. It looks really cute when it is all finished and painted. Here's the video showing how to make it: