Just use some isoprophyl alcohol and your thumbs. Pour some on the LCD where the adhesive is.  Let that soak for a minute then start pushing the adhesive towards the edge of the screen. It takes a while but it works. Just try not to slip and rip the ribbon cable to the board. I've used this method more times than I can count.

As lon as you're using googone and not goof off. The latter likes to eat through stuff sometimes.
I've used googone plenty of times though and it's been fine. Just make sure to be thorough with cleaning it all off when you're done. It gets pretty greasy.

I'm wondering if anyone has ever tried to use GooGone to clean the back of the LCD to get rid on the left over stickum when installing a backlight. I've seen several places recommend rubbing alcohol and qtips but that just seems to end up with qtip fuzz stuck to the back. GooGone is fantastic about removing that sticker gunk but I'm wondering if it might damage the screen.