Per Kester 44 series activated Rosin cored solder, storage must be in a dry, non-corrosive environment. The surface may lose its shine and appear a dull shade of grey. This is a surface phenomena and is not detrimental to product functionality.
Flux cored solder wire has a limited shelf life determined by the alloy used in the wire. For alloys containing > 70% lead, the shelf life is two years from date of manufacture. Other alloys have a shelf life of three years from date of manufacture.
Reference:
https://media.digikey.com/pdf/Data%20Sheets/Kester%20PDFs/44_Global_(14Jun07)%5b1%5d.pdf
Kester 44 series:
https://www.digikey.com/products/en/soldering-desoldering-rework-products/solder/262?k=&pkeyword=&sv=0&pv1989=0&sf=0&FV=-5%7C2797%2C-1%7C117%2C-8%7C262%2C1433%7C397515&quantity=&ColumnSort=0&page=1&pageSize=25
All solders:
https://www.digikey.com/products/en/soldering-desoldering-rework-products/solder/262
It’s worth noting that manufacturers’ shelf life figures for such products are likely to be aimed at ensuring optimal performance in a production environment, and can be interpreted quite generously for other contexts such as personal use. I’ve rolls of rosin core solder on my workbench that are at least ten years old, and have no complaints about the serviceability of either.
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I have the (leaded) 60/40 radio shack solder roll from I’d say 10+ years ago, seems to work just fine for me also on a hobby level, as it appears to have good surface wetting and solid welds. The only thing I can think of would be that it may have slightly more joint resistance as the oxidization on a micro level may be higher? That is a total guess however. 
-Of course any good solder weld shouldn’t rely solemnly on the solder being a conductor
Old solder can be hit or miss, if the solder has been sitting around for years and you find you’re having trouble with cold joints, pushing the solder around like it’s a ball of mercury, this might be the issue. The solder can still be used just keep some external flux around to add to the joint prior to soldering.
For production environments where the chance of a cold joint means the chance of down time and troubleshooting in the field, it’s best to treat the shelf life like a pumpkin and buy new solder or always add flux if it’s after the expiration date.NASA would say add flux always.
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I agree, all reliance on solder should be irreverent and jovial… 
Autocorrect: providing comedic relief since 1995…
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