It's always nice to give someone a sincere and beneficial compliment. Especially one's girlfriend or wife loves to hear nice things, and it is one's duty to bestow compliments on one's loved ones.
First, make sure it is true. Don't tell an ugly person they are gorgeous.
Next, make sure you are being tactful. Don't tell a crying woman she is pretty...it's just weird.
And last, be pure. Have no ulterior motives or shady scheme.
As long as you just say something pleasant from your heart, and the person doesn't hate you, then the compliment may very well be a huge success.
By the way, I really enjoyed your question,
that was awesome Jon! ;-)