There are several china patterns to choose from such as the more traditional Lavender Rose and Tea Rose patterns, made by Royal Albert, and Carnation and Real Old Willow, made by Royal Doulton. There are also several modern styles available. But not everyone drinks tea. You don't want to throw them out but you won't use them to serve tea either.
Teacups make lovely containers for silk or dried flower arrangements.
Choose flowers and greenery that are diminutive in size and complementary to the color and pattern of the cup. Rose buds and tiny ivy makes a nice combination. Sprigs of baby breath would also be appropriate. You could even use miniature carnations. At Christmas, you may consider using small silk poinsettias or holly in a plain white cup.