OK, this may have a pretty targeted audience, I admit!
A long-standing Cambridge service is the weather station on the roof of the University Computer Lab, which was, before that, on the roof of the Olivetti Research building - it must have been running for about 20 years.
I’ve done a custom weather component to pull the data from it, which might be of interest to those in the Cambridge area. It tracks the local Dark Sky report quite nicely:
You can find my component here:
I love it when people do stuff like this, even if it is probably largely a waste of your time, given the limited audience and the fact that it gives very similar results to Dark Sky.
Where else but Cambridge would there have been a weather station operating publicly for 20 years 
Thanks Nick! One thing I learn from this is that I probably don’t need it, since it is generally so close to Dark Sky (which is quite a bit better than the Met Office, for example).
On the other hand, this has been around for a lot longer than most web APIs, and may well outlive many of them!
Data standards have changed, though; JSON, of course, didn’t exist when we set this up; it was a CORBA service originally (for those with long memories). But the plain-text output continues to work well, though I did have to convert wind information like ‘5 knots from the SSW’ into km/h and bearing.
