While it is best to wait until the vines die back, they can be harvested as soon the skin is too hard to cut with a fingernail and the stem is hard and dry. Same holds true for winter squash in general.

Here's what you can do, if you realize you didn't give your butternuts enough time to ripen...

1) Put paper towel down on your window sill.

2) Place your squash "stem up" so they sit nicely and can get enough sun.

3) Take additional paper towel (about 1 piece for every stem you have), wet it, and wrap it around the cut-off stem. Try to do this as soon as possible after cutting your squash off the vine. Also make sure most of the paper towel is where the stem is cut off.

4) To make sure it stays damp, take a piece of foil (I used pieces about 3-4" squared) and gently place it on top of the paper towel that is covering the stem of the butternut...making sure to pinch it tightly around the part of the stem that is closest to the fruit (so the foil should resemble the shape of a light bulb). Make sure the foil completely covers the paper towel.

5) Repeat every day, for about a week (or less if your stems happen to get mushy, mine didn't), to ensure they're getting enough water to keep them ripening.

TAH DAAAAAAAAAAH! Brilliance at it's best.

Thank you.
(I made this up, and tried it, and it completely works!)

Take a look at the bottom side of your acorn squashes. Is there a yellow spot there? Or is it waxy orange? If it's yellow... not ripe. If it's orange... maybe ripe. In either case it's best to wait for the vines to die. I've heard they don't last long in storage, but my experience says they last plenty long. 3 months... no problem. Maybe more but I don't know cuz I ate them all within 3 months.