i'm subletting a room in an apartment in NY.  the girl who previously
lived in the room called me a few days ago to ask if i wanted to buy
her closet, curtain rod, and/or tv.  i asked her "how much?"  i didn't
like the price she was offering, so i said no.  She even told my
present roommate that I told her that I was not going to buy any of
her stuff.  My move-in date was today, Sept.1.  I come in to find
those 3 items all here.  I left her a message saying that i was
cleaning the room, and if she wanted her
stuff, she should call me back to let me know so i could clean after
she moves it all out.  she didn't call back until 6 hours
later...after i had already cleaned the room with the stuff in it.  i told her she
could get her stuff, but only if when she breaks apart the closet and
unscrews the curtain rod, if she cleans up whatever mess she makes
since i spent time cleaning the room.  she said, "no."  To make a VERY
long story short, she refused to do the cleaning, so i told her she
can't get her stuff since she left it in the apartment and my move-in
date was today.  I was willing to not throw it out and leave it for
her to pick-up as long as she cleaned up whatever mess she left
behind.  The room wasn't left to be her storage space.  She KNEW i
wasn't taking the furniture but she assumed that if she left it here,
i'd offer to buy it since it was already here.  She was wrong. 
Basically, I told her that she can't come into my room w/o my
permission.  She said that she could do whatever she wanted.  Now my
question is...Legally (i know it's not taking the "high road" but that
isn't the point)...but Legally, could i throw out the stuff she left
behind in the room?
And Yes, I know this all sounds very petty.  That I should just let
her take her stuff and be out of my life, but I'm not asking for moral
judgment.  I'm asking for legal advice.

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It is really the landlord's responsibility to take care of these
matters and you should have brought this up at move-in (there's a
lesson in acting like a grown up for you-- don't take possession of
property unless it meets your standards; and for goodness sake, take
pictures at move in and move out with a current newspaper as proof!).
If you want to foist it off on him/her, you probably can; box up the
stuff and present it to the landlord.

If you resort to "self help" you may open yourself up to liability,
something grownups try to avoid. To protect yourself, send the
previous tenant a certified letter (return receipt requested) either
giving her a reasonable deadline to pick up the stuff, or informing
her she has effectively abandoned her property.

In a sane world belongings left behind by a previous tenant would be
considered abandoned; after all, she isn't paying for the space the
stuff is in, right? But in the US we have all sorts of laws to protect
idiots, morons, dolts and dweebs. Anybody not up to speed on the
latest legal silliness should look into Rhode Island's new rebate law.
Just G00gle RI, rebate, and law.

This is NOT legal advice and you probably won't get any here. And if
this is the biggest problem in your life, count yourself fortunate.

Just use it for free until she comes to collect it.

I agree with Mark that it is the primary lessee's obligation  - as
your immediate lessor -  to deal with the problem.  I expect that the
owner of the apartment will say the same thing.

The answer to this question deals with the problem in another state,
but the concept is probably the same:
http://answers.google.com/answers/threadview?id=714097

Perhaps the relevent NY law can be found on this site:
http://www.megalaw.com/ny/top/nylandlord.php

markvmd-ga:   He/She states that he told this person "no" (line 4), he
did not want the furniture.

For the previous lessor to assume that this new person would move-in,
and at that time, want the furniture is ridiculous.  Why should he box
up a wardrobe/dresser, that may be both heavy and large, for the
person who left it behind?  Now, I don't know about you, but in
roommate situations in NY, you want to move your stuff in and not
worry about anything else.  For him to be forced to have the old
lessor coming in 2-3 days after move-in to break apart some closet and
uninstall a curtain rod that will end up in the trash--after all of
the new lessee's own property has been moved in and arranged--is not
something you nor anyone else would like to have happen.  A phonecall
to let the old lessor know that her things should be out of there
seems sufficient.  A text message should seem sufficient.  Why should
the new lessee go through all that trouble.  How long should he have
to wait for the items to be removed?
Also, the comments mention that a "reasonable" amount of time should
be given to the old lessor to remove the items.  If this old lessor
knew she had to have everything moved out by a certain date with the
knowledge that a new tenant would be moving into the room, is that not
a reasonable amount of time?  Shee has only left behind what she hoped
the new lessee would buy (although she knew the new lessee would not
buy).  Shouldn't the new lessee be allowed to remove and discard
excess items from the room?

Also, I assume that sublet rules/laws must be different from regular
housing laws.  A new sublettor can move-in the day of a move-out (by
the old sublettor) whereas a new lessee moves in after the
landlord/super has emptied out and cleaned the entire apartment
(approx. 2 weeks).  Since this is the case, there is no notice to
remove belongings other than the notice that this person must empty
out before the new sublettor moves in.  So how do general housing laws
apply to this situation?

Angrytenant, read what I said:

"It is really the landlord's responsibility to take care of these matters..."

and

"If you resort to "self help" you may open yourself up to liability..."

Note the word "may."

Now let us assume (assuming, foolish mortal, is how problems get
started) that the prior tenant takes you to small claims court and
says, "But, your honor, the new guy told me in a phone call I could
keep the stuff there when I explained my situation. He was really
sweet about, too."

Whatcha gonna do? Tell the judge you're really not a nice guy? Get
involved in "he said, she said"? Curse the Heavens for not following
my advice and sending a certified letter for a whopping three bucks?

Certainly it is unlikely to happen that way because the landlord is
the one to get sued... unless the landlord says, "Hey, the new tenant
worked out a deal with the old tenant." Now you're potentially back in
the dock.

So listen up, kid. Protect yourself. Drop the tenant a certified
letter telling her to get the stuff out or you're gonna toss it. You
might want to try this ploy with the landlord first. Yep, it's gonna
be a pain in the butt to you but YOU took possession of the things and
you MAY have to excercise certain care with it. Maybe not, either. You
wanna take the chance? Be my guest.

UPDATE:
Sometimes, not giving in can be the solution to these types of
problems.  The old tenant decided that it would be more trouble for
her to move these items out.  They have been left for the new tenant
to do with as he wishes.  The End.