What actually happens over time
Aroma compounds are volatile and leave. Oxidation continues slowly even in a sealed packet. The result is not an unpleasant tea so much as a duller one: the top notes go first, then the sweetness, and what remains is flatter and more generically tea-like. Green teas fade fastest because so much of their character is fresh aromatics; heavily roasted and fermented teas fade slowest.
Rough windows for flavour
Japanese green tea is at its best within a few months of harvest and noticeably tired after a year. Chinese green tea is similar, slightly more forgiving. White and oolong tea hold for a year or two. Black tea holds for two or three. These are about when the tea stops being what you paid for, not about anything else.
The teas that improve
Sheng puerh, some heicha, aged white tea and certain oolongs are stored deliberately for years or decades and change substantially — this is the entire basis of the aged-tea trade. That storage is a controlled activity with specific humidity and airflow requirements, and is not the same as a forgotten packet in a cupboard.
What TeaHQ does not say
This site does not make statements about whether anything is fit to consume, and nothing here should be read as one. The question answered above is whether old tea will taste like the tea you bought. Storage conditions — airtight, dark, cool, away from strong smells — are covered separately and matter more than the date does.