Depends on the variety. 'Bartlett' for instance ripens on the tree, like an apple. Look the other up to see what it needs - a percentage of European pear cultivars do need to be picked before maturity and ripened in cold storage in order to "finish" successfully.

ALL pears should be harvested before they are fully ripe!! They ripen from the inside out, so when they feel ripe to the touch on the tree, they are already starting to deteriorate on the inside. And they do not need 'cold storage' either - just regular countertop temperatures.

You can tell when a pear is ready to be picked off the tree by judging size and firmness but also by holding the fruit in the palm of the hand and gently lifting. It should come away from the branch easily and without effort.

Update -

Ok here's the scoop - the earlier ripening pears which I picked were about 60% infested with a boring critter in the center. These pears were mostly edible on the perimeter where the flesh was still good (not brownish). As pears fell off the trees, these pears were also ripening up a bit early, looked good on the outside, but again most of them had bad cores. The latest pears which hang on were mostly untouched by boring critters/ center rot and were/are very good, sweet, and very juicy, no rot present.

I have stored about 50 of the premo pears in the fridge so they'll ripen more slowly and hopefully be enjoyed up until Xmas time (similar timing for the persimmons). The last pears on the tree, if they haven't been bird pecked or bug bitten, are the best ones to be had as long as the don't over ripen. I don't spray these pears but they were so plentiful this season that it didn't matter.

My pears ripen from the inside out so if I wait until the pear starts to soften noticably it's already way overripe. I've found when the tip of the pear just starts to soften thats the right time to pick.