In the card game Magic the Gathering, can a spell be played with no valid target?

A friend of mine runs a deck involving the ability Storm, and he frequently plays spells for the purpose of adding to the Storm ability, however some of the spells do not have valid targets, but he plays them saying that the spell is played so it adds to his Storm, is this allowed?

No. It is not legal to play a spell if there is no valid target.

Relevant section from the Comprehensive Rules:

409.1c If the spell or ability requires any targets, the player first announces how many targets he or she will choose (if the spell or ability has a variable number of targets), then announces the targets themselves. A player can’t play a spell or ability unless he or she chooses the required number of legal targets. The same target can’t be chosen multiple times for any one instance of the word “target” on the spell or ability. If the spell or ability uses the word “target” in multiple places, the same object, player, or zone can be chosen once for each instance of the word “target” (as long as it fits the targeting criteria).

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