Western Union is probably the biggest, oldest and most well-respected money transfer agency in the world. Millions of people use it every day without any problems.
However, most of those people will be (for example) migrant workers sending money home to their families. They know, and trust, the people whom they're sending money to. For them ,the system is perfectly safe. As Hymie indicates, you should never use services like Western Union or Moneygram to pay strangers for internet purchases, as your money can easily disappear, without trace, into a black hole from which there is no return.
Chris