From what I've been reading, sounds like more LL's are asking for 2 months, sometimes even handing over a small amount just to show interest. But then again most apt posts I've seen where they actually specify the deposit amount, is usually stated as one month.
In the US it greatly depends on the state. Some depends on the length of term, if the place is furnished (some states allow a charge up to 3 months if furnished) or unfurnished, if it is a single family dwelling etc. The 2nd to last city I rented from in the US asked for first, last and security deposit. Plus LL's can charge for an application screening fee to check references and credit report. Some allowed you to submit your own credit report from the 3 big organisations though. Not too mention in some parts of the US you don't really have too many amateur LL's just renting out one place.