Why do some Hassidic Jews wear little boxes on their foreheads?

They are called phylacteries, and they contain parchments with handwritten prayers from certain books of the Old Testament. (They are also sometimes called tellifin or telliphin.)

They are worn because of the commandment God gave in Deuteronomy to bind Scripture on the forehead. It's a part of the religious practice of Jewish men: aka, a mitzvot or righteous duty.

It's not just Hassidic Jews and they don't wear them all the time.

Male Jews have a mitzvah they have to do called to put on tefillin--the leather straps and the boxes you speak of. One box goes on the arm and the leather straps wrap around, and one goes on the forehead because of the verses "and you shall bind them on your arm and between your eyes, and they shall be tefillin before you." (That's just quoting from memory, the actual verse might use slightly different wording.) It's a mitzvah all Jews are called to perform every morning (except on Shabbat.)

Why do Christians practice ritualistic/symbolic cannibalism? Same reason, it's a part of their belief system. Specifically, there is a scripture that says to bind the law on your right wrist and forehead (or something to that effect).

Not just Hasidic Jews, anyone keeping the commandment listed above. They are called tefillin, and have paragraphs from the Torah in it. They are worn Sunday-Friday (barring exceptions) during morning prayers.

What Do Jews Wear

The phylacteries on forehead and Arm carry scraps of paper with scriptures on them and if you check the door sill of their homes you'll probable find a mezuzah which is a small box with more scriptures in it.

Big Hug, menome b

In obedience to this passage of Scripture:

" Hear, O Israel: The LORD our God, the LORD is one. Love the LORD your God with all your heart and with all your soul and with all your strength. These commandments that I give you today are to be upon your hearts. Impress them on your children. Talk about them when you sit at home and when you walk along the road, when you lie down and when you get up. Tie them as symbols on your hands and bind them on your foreheads. Write them on the doorframes of your houses and on your gates. "

Deuteronomy 6:4-9

This came up in a different question, really quite interesting...

http://en.wikipedia.org/wiki/Tefillin

You mean "phylacteries"?

Check out the answer above mine.

http://en.wikipedia.org/wiki/Tefillin