No, the best used by date on alkalines is an estimate of when the battery will fall to 80% capacity just sitting on the shelf. So long as they aren't physically leaking, they may be worth keeping for years after the expiration date. Me, I'd probably keep anything that measured 1.3V or higher....but depends on how picky your devices are about voltage input.
I disagree, for Best brands you might be able to keep them 1-2 longer years (if it's unused), but that's not always a case and I won't start about POS non name crap, I had quite a few "accidents" that cost me alot when batteries leaked like 3-6 months after expiration date and I'm talking about quality brands, not every battery is identical thus outer shell of the battery might have different thickness or other imperfections which might cause if to erode to fast and leak.
Also I've seen plenty of crappy batteries that start leaking just before/after "best by date" while they are still in original manufacturers package and no they are not fakes.
Usually if battery was running for 2 years and it expires I trow it away (I usually check all batteries every year to make sure they are not leaking), if battery was never used I might use if for a few months in a device that cannot be damaged beyond economical repair if it leaks e.g. flash lights, and other cheap stuff, but never in "expensive" tools.
P.S by batteries I mean alkaline cells.
P.P.S Note: I'm not trying to be rude, I and my dad just had to many "accidents" in 10-20 years...
Edit: Also Make sure that batteries don't stay in warm/hot humid places, 17-20C is best, but check with the manufacturer what they recommend for your particular battery.