Laccaria ochropurpurea
Several obvious traits help identify this sturdy, late-summer mushroom commonly called the Purple-Gilled Laccaria:  
When very young, the little mushrooms often have disproportionately tiny caps compared with their fat, swollen stems. Even when mature, the strong, fibrous stem supports a cap that doesn’t quite seem big enough for the thick stem. Also, the beautiful, purple gills, widely spaced beneath the cap, eventually get dusted with the diagnostic white spores with age. They’re easy to recognize, once you’ve seen a bunch of them.
Compare against the Wood Blewit or toxic Cortinarius look-alikes.