Our dance shoes. They are our greatest support and our most basic need in dancing, and yet eventually we throw them out for something shiny and new.
How long a pair of shoes lasts depends heavily on how much you dance, what brand your shoes are, and to a lesser extent what kind of figures you dance. On average, I find myself buying new shoes annually, though if accidents don't happen and I break my shoes in well, I can probably stretch that to 15-16 months. That is with Supadance shoes and spending on average 10 hours a week wearing them. I would kill shoes from brands like Dansport or Capezio a lot faster. They aren't bad shoes--I actually quite like my Dansport pairs. The cost of them being less expensive, however, is that they are less resilient.
So how do you know when to go looking for a new pair? Competition shoes can stay competition shoes until they are too ugly to be on the floor. Depending on how well you maintain them, that can be a very long time. Even satin shoes can be washed to remove the worst spots, though they won't be as shiny afterwards. My practice pair of shoes actually determines when I go shoe-shopping; when the practice shoes die, the competition shoes are demoted to practice shoes, and I buy a new pair for competitions.
I personally know that my practice shoes are dead when I can't stand up in them. The front of standard shoes, from the ball of the foot to the toe, is actually quite soft to allow the dancer to easily rise to the toes. The area around the ball of the foot gets softer and softer with wear, and eventually the sides will be too soft to stay properly on my foot. If I start having significant issues with my balance over more than one practice, I'll thoroughly examine my shoes to check for signs of wear. Heel tips can be replaced and ripped satin is typically not a problem, but if the sides have gotten floppy, the shoes are dead.
Another related sign of death is suede on the bottom of the shoe compressing to nearly nothing. When this happens, your shoes start sliding everywhere. Brushing the bottoms of your shoes will help offset this, but also rips up the sole a bit and is only a temporary solution. This is a subtler sign of the end, but it is more pertinent for men's shoes. The fact that men's shoes lace means they can survive more change in the size as the shoes stretch without needing replacement.