I am looking for charities located in Manhattan, who are accepting
non-monetary donations. The prime requisite is that they be willing to
come collect the items themselves. I am not able to deliver or ship
items.

Items which I am looking to donate include: videos (used and new, and
in large quantities), women's wigs, clothing.

I would prefer to donate to charities which cater to cancer or AIDS
(research and/or assistance to the ill), or to orphanages. I am hoping
to get contact information for several organizations, if possible.

If a researcher doesn't find the cancer/orphan related charities for
you, as a New Yorker, I  can highly recommend a wonderful charity: 
MATERIASL FOR THE ARTS.

It's run by the City of New York's Department of Cultural Affairs. 
The'll send a truck to come pick up whatever you have to offer.  It
all goes to a giant warehouse where about 3,000 non-profit arts groups
and schools around the city come and take what they need for their
theater/dance/art /music /whatever / creative projects.   Anything
goes: boxes of old buttons, costumes, kitchen supplies, 300 left
shoes, air conditioners, 100 yards of red ribbon, a moose head, a
typewriter, you name it -- somebody is going to want and need what you
have.

I've given them all sorts of things and last year donated a piano. 
There was a waiting list of about 25 groups that wanted one and I got
to interview and choose who it went to.  (I gave it to a small
after-school theater group that performs for Firemen /policemen and
families who lost loved ones on September 11th. )

Materials for the Arts will come pick up your donations and you'll
recieve a letter and receipt for tax purposes.   (And very often a
thank you note from the group that chose your items).

here's their website and another site with a nice article about them:

http://www.mfta.org/home.php

http://newmedia.jrn.columbia.edu/2004/issue4/story3/

Thanks very much for the suggestion!