年寄り:としより; ('70s and up) this isn't rude per se, but if you want to dismiss or belittle what an old fart just said, this is the word you use.

老人;ろうじん;('70s and up) old person

年をとった:としとった:('70s and up) just like 老人 but it's an adjective.

年輩:ねんぱい; this is the most polite - you can even use it for someone in their '60s - but it's so formal you can't say '年輩の人’, you have to say ’年輩のカタ’