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About as accurate as any other Fermi Estimation
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Pretty accurate for climbs without much wind to account for. PowerTap hub and strava agreed to within about 10w for a run up Mott St. You'll need to be accurate with your bike and rider weight though.
Totally unreliable on the flat or with wind to account for.
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Definitely ignore it for any short (under 1km) segments, especially if it's an uphill bit after a downhill. For example, look at the overall leaderboard of this segment:-
https://www.strava.com/segments/4020943/leaderboard?filter=overall
I know I didn't average 550W for 1:20 there.
Also, it's only as reliable as their elevation model, which can be wildly out in various places (so something that is actually downhill is shown on Strava as uphill, which completely screws their estimation, and vice versa).
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gbj_tester
dbr
Greenbank
@J0nathan
How accurate is the power estimate on Strava?