The avowed purpose of alliances is to provide for national defense.However, entangling alliances led to a world war in 1914.Could alliances...

International relations theorists call this the "security dilemma."  It is the idea that things that a country does to make itself secure really make it less secure.  Country A acts to protect itself (say by making an alliance) but Country B thinks that the alliance is meant to harm it and it becomes more likely to attack Country A.  So definitely yes -- this can happen.

I do not really think that current alliances are likely to lead to war.  I think current alliances are much looser than previous ones, mostly because there is no major threat to the larger countries of the world.  The US is not afraid of Russia, for example, and is not likely to be pulled into war because of its NATO alliances with Eastern European countries.