It's hard to know without a picture or knowing where you're located. You say it is not a phlox, so that rules out creeping phlox (Phlox subulata), which has a shock of color when in bloom and has needle-like leaves. Vinca minor is not usually THAT floriferous and often is grown in shade.
I assume it is not a weed such as creeping charlie (Glechoma hederacea) or crown vetch, given that people are cultivating it.Might it be ajuga?Under the circumstances, I suggest you take a sample to your local garden center or Cooperative Extension Service office, preferably while the plant is in bloom.