This can depend on why you’re wearing the suit. If you’re going out with your friends, you could get away with something like a bright yellow or a bright blue. Something bright would be bad for work, though.
For work, try to go with a more subdued tie color. Perhaps a lighter blue. Do not wear black or brown on a navy blue suit; they are too neutral. They will blend in.
For a wedding or a date, perhaps go with something that sets your eyes off. This is a years-old trick that works wonders for anyone trying to create interest. Do it if you want to look dreamy or handsome. Try to avoid this one for work, though, since it may come off wrong to others at the office.
Red, green and pale blue look good with navy. However, be careful not to choose too strong a color or you may look garish rather than refined. Navy on curtains, say, or a child's dress, contrasts well with bright yellow but this doesn't work well with a navy suit.
The fact that you're wearing navy suggests you want to make a fairly sober effect on those you meet, or to look professional and workmanlike for an interview or board meeting. If you are very young, you can risk a bright color if you're just mixing with your mates at an event, but if it's a wedding or an interview, play safe and go for a bluey-green. If you want to look handsome, match your eyes. They are unlikely to be red or yellow!