Ama bu filmi izlemeyi çok istiyorum. 
I do not understand why there is İZLEMEYİ,isn´t there suppos to be İZLEMEK.

Yes but...

look here, tunci´s post nr 5:

                     http://www.turkishclass.com/forumTitle_54128

After reading tunci´s post, I would like to add a bit;

For the verb istemek, if it has an adverb before "istemek", then it sounds better with accusative -i suffix on the other verb. In this example, the adverb is "çok". So;

"Gitmek istiyorum" is good. "Gitmeyi istiyorum" is good as well. But with adverb;

"Gitmeyi çok istiyorum" sounds much better for my ears. I don´t know if there is such a rule but if I say "Gitmek çok istiyorum" it sounds strange. Maybe that is correct as well, but it is like a baby´s sentence who is still learning to speak.

Other examples;

Televizyon izlemek istemiyor.

Televizyon izlemeyi pek istemiyor.

Su içmek istedi.

Su içmeyi bir saat önce istedi.

But if adverb can be in another place in the sentence, then without -i sounds well too:

Pek televizyon izlemek istemiyor.

Bir saat önce su içmek istedi.

There must be a reason because you can describe it so clearly, caliptrix.

Maybe because the object is physically separated from its main word. Too far. It is kind of more secure to mark it with ACC.

By the way, I wrote this;

So sometimes you cannot put adverb to another place because the meaning goes different;

Gitmek istiyor => Gitmeyi çok istiyor

But what if this adverb goes to the verb "gitmek" because it becomes just before it:

Çok gitmek istiyor

So this sentence sounds like he wishes to go too much, as going too much. Not "too much of want", but "too much of go"

So that becomes weirder

Abla,caliptrix, thank´s a lot for help!! But,is izlemeyi(for example) using just after adverb,or there is some exceptions??