What's the proper word for a person waiting in a queue?
Someone who waits in a queue is a queuer1.
For example
Look at all those queuers queuing! I wonder what they're waiting for.
1 "queuer, n.". OED Online. June 2012. Oxford University Press. http://oed.com/view/Entry/156388?redirectedFrom=queuer (accessed July 31, 2012).
In queueing theory, the common word to refer to people waiting for service is customers.
In normal speech it’s quite common to simply refer to “the people in the queue”.