You come home after two weeks away. Your cat looks up, blinks, and goes back to washing a leg. Has it forgotten you? Almost certainly not. That's just the welcome.
The 16-hour myth
You may have read that a cat's memory lasts 16 hours. Futura Sciences traces that number back to a 1960s animal psychology book and says current research doesn't support it. There's also no study that gives an exact expiry date for a cat's memory of a person. As Catster points out, it's hard to test, and most of what we know about long-term feline memory comes from owners' reports.

What has been tested
In 2013, University of Tokyo researchers played 20 cats recordings of strangers calling their names, then their owner's voice. Fifteen cats got bored of the strangers and then perked up again at the owner. The cats could tell the difference, but they showed it by moving their ears and heads. They didn't meow or move their tails. In other words, they heard you perfectly and chose not to reply.
Later work found that cats can tell their names from similar-sounding words, and may even keep a mental map of where their owner is, based on voice alone.
So how long?
Specialists quoted by Futura say the memories that stick are tied to emotion, and that scent, voice and routine matter more than your face. Those memories can last months or years. Catster collects reunions after 2, 7 and even 12 years, though these are anecdotes rather than experiments.
Bring a treat anyway. Science doesn't require it, but your cat will.