Difference between ほしい and ～たい form

ほしい means to want/obtain an object. A noun normally precedes ほしい.
～たい means to feel-like/would-like a verb. This (obviously) modifies a verb.

While both phrases express a desire (usually the speaker's), who is to perform the desired action is dependent on which 'want' term is used.

In these examples, when the て form of a verb and ほしい are in the same sentence, the person performing the desired action is someone else.

Examples
ピザが食べたい。I want to eat pizza.
ピザがほしい。I want pizza.

車を買いたい。I want to buy a car.
車がほしい。I want a car.

あの新しいB'zのアルバム買いに行きたいな。I want to go buy that new B'z album.
あの新しいB'zのアルバムほしいな。I want that new B'z album.

それを食べたい。I want to eat that.
それを食べてほしい。I want you to eat that.


バスケがほしい。I want a basketball.
バスケを遊びたい。I want to play basketball.
バスケをパスしてほしい。I want you to pass the basketball.


バスケがほしい？Do you want a basketball?
バスケを遊びたい？Do you want to play basketball?
バスケをパスしてほしい？Do you want me to pass the basketball?


何をしたい？What do you want to do?
これを食べたい人はいる？Is there anybody who wants to eat this? (Note: relative clause: これをたべたい）


Source:
http://www.guidetojapanese.org/forum/viewtopic.php?pid=57224
http://www.anime-planet.com/forum/japanese-discussion/13016-i-want-ga-hoshi-versus-tai-form.html