Generally we use "splurge" to indicate doing something to excess, like spending a lot of money or eating a lot of food. Examples: During our vacation in Paris we decided to splurge on a fancy French restaurant. She used her tax return to splurge on several new pairs of shoes. He has little income and cannot afford to splurge on anything.

Tony's answer is good. In the UK we also use the construction 'to splurge out '. I guess its more emphatic, showing it really is doing something to excess. So each of Tony's examples would work with 'splurge out' too, as well as 'splurge' by itself.