tl;dr: 5-10 years in the absence of other info. Less if you need top reliability or are tough on hardware, more if you're buying top-quality gear and not stressing it much. How heavily and at what duty cycle has your PSU been loaded, and do you know the model?
The main wear component in a PSU should be capacitors, which are mainly worn out by heat (including heat created inside the caps due to ripple current). A high-quality, efficient design that's usually run at low load on cool air should last all but indefinitely. Cheap capacitors, more heat, and more power each result in a lot more wear.1
A good PSU should be decent for 5-10 years in a gaming machine, even if heavily loaded. 24/7 use could burn up caps much quicker, though.
In a well-engineered PSU, everything else should easily outlast the caps, but in a world where 5 cents on a bill of materials matters, things don't always work out that way. These failures will be much tougher to predict, but most probably still have some dependence on heat and power.
There are a lot of parts in a PSU that could theoretically break some other part of a computer if they failed. Most often they don't, and I find that a small miracle. I doubt that old PSUs going out with a bang are much more likely to take anything with them than new ones, but with that said, older PSUs with worn caps will be noisier and more stressful on components in normal operation.
To answer the original question, yeah I would consider PSUs to have an expiration date, but it's tough to say what it is without more info. There are rigs I'd be comfortable with pretty much indefinitely, and there are rigs I'd feel iffy about at two years.1
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has an example of how heat and power affect caps. The stuff in that datasheet could be used as a main APFC cap in a computer PSU. The usual rule of thumb is that a 10C increase halves the life of a cap.