It depends entirely on the game. If making an attack is just one die roll, then you could easily accommodate seven in a round without slowing much down, especially if they all went against the same target. If each attack required choosing a new spell or power, with its own secondary effects and attack bonuses, then you really wouldn't want to go over one in a round.
According to some of my acquaintances who are big fans of 4E, the biggest thing that slowed the game to a crawl was everyone using multiple attack powers every round, because of minor action attack powers and reaction attacks.