is your red darker like a brick red or more middle of the line?
you could try some oranges or golds...or go more in the creams/ivory and even yellows...its going to depend on how dark or light of a room you are trying to create...blacks, browns and tans go well with some reds...as do the more olive greens...and of course theres always patterns to bring in several colors...if your counters, cabinets and appliances are darker, then you'll need lighter shades to create a balance. you can always bring home some fabric samples and scraps to give you an idea before you buy. I saw your other thread asking about grapes etc... the Tuscan theme is still popular and would incorporate those colors and the wine bottles/grapes... or you could check out some Spanish or Mexican themes that would match your reds. Look around on hgtv.com or go to a store that has displays of kitchens so you can see some already decorated.
have fun and try new things...I had the country kitchen for years and went for a big change using accessories and textures--its kind of a Tuscan--meets Tex Mex...lol..lots of bright colors, the bottles with the pickled peppers and brightly colored plates and bowls, jars of pasta etc..
If you have a Home Goods Store they have tons of choices.