Digimon Tamers, Accel World Recommendations
The stories revolve around a game that takes on a bigger meaning then just being a game. Real world friendships are formed and in the long run goals are formed as well. They also deal with digital worlds and getting away from reality, not to mention having abilities that can actually effect the real world in a positive or negative manner.
Similarity drawn in that both series revolve around fighting in a digital world. Accel World has inklings of romance while Digimon Tamers vaguely hints this. However, both series offer plenty of action.