One week's pay is often held up as typical, but as a nanny I have received all over the board. It depends on a lot:
1) How long her hours are (simply because genuine appreciation is key to staving off burnout)
2) How long she has been with you
3) How well you pay--if you are paying a high hourly and can't swing a week's pay that should be understandable
4) The big one: how well does she actually perform? There is a big difference between doing something fairly token (gift from the kids worth $30-50 and a nice card) versus really going all out (large cash gift and/or present AND the thoughtful card) and the difference should be whether you are really pleased with your nanny or just meh. Does she do her job with a positive attitude? Does she provide reasonable flexibility when you really need it? Does she go above and beyond in little ways? Brass tacks: is your family life truly enriched because THIS PERSON is your nanny? If so, then focus on thoughtfulness and genuine expression of gratitude (i.e., tell her what you appreciate and how much in writing), then give what you can. An awesome nanny isn't going to quit because you didn't shell out a huge pile of cash.