Vivien's Stampede is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

Each creature you control gains vigilance, trample, and melee until end of turn. (Whenever a creature with melee attacks, it gets +1/+1 until end of turn for each opponent you attacked this combat.) At the beginning of the next main phase this turn, draw a card for each player who was dealt combat damage this turn.