It depends. When you are talking about sneakers are you talking about your every day sort of run around doing errands shoes? Or are you talking about running shoes that you use to run 10 miles per week in? Or cross trainers that you go to the gym and do aerobics classes in? Or shoes that you only throw on once a week to walk around the yard or go to Target, or wear around on vacation?
It really matters how and how much you wear them. For running shoes that you are actually running in, age matters less than mileage! 500 miles tops, maybe 300 miles depending on how long that takes you.
For "I'm just throwing these on to go to the store b/c flats/heels are not practical" types... I could wear those for a couple of years, unless they get worn doing something dirty and they start to come apart or feel less supportive, or get smelly.
If I wore canvas sneakers (keds, converse, etc).. then I'd toss them the second they started getting worn spots in the canvass. It happens pretty quickly from what I can tell from my daughter's shoes. But then, she wears them pretty much every single day, everywhere she goes. And she's rough on them (she's 13).
If you have any sort of foot problem, then I would be more particular about how long I wore them and check regularly to be sure they were providing the level of support needed for whatever condition I had. If this is the case, then check with your doctor (who is advising you about said condition) and get a recommendation about how often to change them.