In sorting out my aunt’s affairs I found some 40-year old sparklers in a drawer a while back. Just sitting there in a drawer of other junk. Not being entirely sure if they were safe, I rang the local council’s Waste Disposal department and they said that it was safe to put them in the bin. So I did. And I haven’t heard of any rubbish trucks going up in smoke.
But thinking back on it, I’m not so sure it was right. Was it safe? And what if I come across gunpowder-based fireworks?
Toss them into a bucket full of water over night, break apart, drain the powder into a bucket of water and throw the whole mess into the dumpster. It’s not like 40 year old sparklers are going to blow up a garbage truck. Ditto just about anything you find short of a grenade. The older they are, the less likely they are to go off even if you lit them. Black powder stuff, I mean. Military-grade is a whole 'nother story.
Be assured that if I do find military grade stuff, which would mean a bomb - not impossible as the place was bombed in WW2 - I’ll be on to the professionals PDQ!
I agree with the above but just a curiosity side note - ammunition has an astoundingly long shelf life if it is kept dry and there are vast caches of old ammo stored around the world. I have shot at least a few of rounds of ammo from WW1 and the gun dealer trade magazines always have cheap ammo from the Korean war and up for plinking (my father is a gun dealer). It is pretty cool to open up a box of ammo that is older than your parents or maybe even your grandparents and see it work. It does have a higher percentage of misfires but, overall, it is cheap and works just like it did back on the day.
Why on earth would you throw sparklers away? 
For some folks, sparklers no longer hold enough thrill to bother waving them around. I’ve gotten really jaded about all that poppity-bang stuff. One summer, I spent many evenings out in the yard with my friends, throwing firecrackers at each other. We cobbled together model rockets with cherry bomb warheads. We booby-trapped traffic cones with cigarette-fused fireworks. We made calcium carbide water balloons for the acetyline fireballs. One of my friends, bless his heart, was seriously fascinated with fire. After that summer, consumer grade fireworks weren’t very entertaining for me.
Now, if sparklers make you happy, go for it. Write your name in the air. As for me, I won’t foul the air with something that doesn’t make me happy.
I forgot to answer the OP. Fireworks will keep a long time, especially if sealed. I used some 10 year old roman candles, poorly sealed, but stored indoors, and none were duds. I have about a hundred firecrackers in a coffee can, older than that, and they’re as reliable as they were when new. That is, one in 30 or 40 might fizzle instead of bang.