There may be a little buildup of oil or something on the grips or bars. Try to clean the grips in hot water with dish soap, maybe scrubbing the inside with a bottle brush. Then give the bars a good cleaning also. Then if that doesn't work, use some tape on the bars to provide a good surface for the grips. Glue might require you to cut them off later.
After a good cleaning, I have sprayed some brake-kleen into the grip and fairly quickly wiped or blown it out. It seems to freshen the rubber a little and make it tackier.
I use Aquanet hairspray for this. Aquanet is one of the stronger sprays and goes on slick to slide on the grip, but turns tacky to keep it in place. Good results on every bike I've tried to far.
Yeah, they do... and it's good stuff for keeping the grips on, but not so much if you wish to remove/reuse your grips. I wanna +1 all the hairspray fans; that'll give you some tackiness, but you can still remove the grip without destroying it.
Wrap a quick spiral of electrical tape on the bar where the grip would go. This increases the effective diameter of the bar enough that most "loose" grips will fit snugly again. For really dry and loose old grips I'll overlap the tape a bit, but for most grips a single spaced out wrap will work wonders. Easy. Cheap. No glue required.
Cheers, Geoff
Not sure if this will work on your old stretched out grips, but WD40 works well for installing grips. Takes about a day to dry, but they will be firmly stuck on after that. Normal removal tricks work if you need them back off. I know,,, sounds wrong.. but give it a try sometime.
I have used a thin layer of contact cement on one surface. To get them off I put a small screwdriver alongside the grip and bars and spray WD - 40 in there and wiggle the screwdriver around while twisting the grip. Seems like a lot of solutions depending what everyone has on hand.