Litter box avoidance is the #1 reason cats are surrendered to shelters. However, most issues are preventable with proper set-up and maintenance. The rule of thumb is: one box per cat, plus one extra.
Size and Type
The box should be 1.5 times the length of your cat. Many commercial boxes are too small. Covered boxes trap odors (good for you, bad for the cat) and makes them feel trapped. Open boxes are generally preferred by felines.
The Scoop Routine
Scoop daily. Replace litter completely every few weeks. Cats are fastidious creatures; forcing them to step in a dirty box causes stress and leads to accidents elsewhere.