Models can fight if they are in base contact with an enemy model when it is their chance to attack, even if the bases only touch at the corner. Even models attacked in the side or rear may fight (though the models are not actually turned to face their enemy).
If a model is touching more than one enemy, it can choose which one to attack when it is its turn to strike. If a model has more than 1 Attack, it can divide its Attacks as the player wishes so long as this is made clear before rolling to hit. For example, if faced with an enemy hero and an ordinary enemy warrior you might decide to attack the warrior because he is easier to kill, or you could take the outside chance of slaying the hero.
In the case of cavalry mounts that have their own Attacks, such as Warhorses and Giant Wolves, the rider's Attack and the mount's Attack are worked out separately and can be directed against different targets.
In any case, models in base contact with the enemy may not refuse to attack their enemies!