According to Judaism illicit relations are forbidden. I always thought that the way one can control his lustful desires is by marrying.

In the *Garden of Peace*, Rabbi Shalom Arush says that a man cannot be a giver if he has lust towards his wife. That is, he should nullify all his lust towards his wife and only focus on giving to her.

Is this opinion unique to the Breslov way of thought or are there other opinions that support this idea?
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This discussion centers around the mishna in avos towards the end of chapter two (either mishna 12 or 17, depending on your print) "all your deeds should be lishem shomayim". 

Rambam offers two different approaches between his pirush on the mishna and in his shmona perakim, which is echoed in the two different approaches in the shulchan aruch brought in shalom's answer. See there and the sources in Shalom's sources for a better understanding.

There is also the gemara in Bava Basra 16a which praises Avraham for having never concentrated on Sarah's beauty, brought in Rashi on Lech Licha 12 11. This would give credence to the no personal enjoyment approach.

This is all Midas Chasidus though. A possibly unattainable goal for which the true benefit is gained simply by a different approach to life. There are many examples in the Talmud where a wife's beauty is appreciated for shalom bayis. In fact the seffer chasidim says it is not allowed to marry someone one finds unattractive as he will spend the rest of his life secretly praying for her to die.

So as with all Midas Chasidus, a disclaimer is in order, not to ruin the main mitzvah while chasing chasing the extra credit. Especially when this mitzvah involves another human being who might not appreciate the lisheim shomayim approach, see the parenthetical story.

(Sad story disclaimer: I had a friend in yeshiva who was the type of masmid who actually learned in his sleep. Seriously. Actual gemara came out of his mouth in his sleep. He impressed all of us cynics. Well, a couple of years into his marriage his wife asked him\* what goes through his mind when they were together. He told her all his higher kavanos and all his lisheim shomayim intentions. She divorced him and took the kids. 

* I know because this wife's confidant was another friend's wife)
There are some *very, very* different views on the subject in different sources. [More is discussed here.](https://judaism.stackexchange.com/a/33902/21)

Satmar thought has similar language, by the way. And many other groups feel that's unworkable.

The Shulchan Aruch in Or HaChaim uses very strong language about "only for her", but in Even HaEzer that does not appear. Most notably, the Aruch HaShulchan modifies the Shulchan Aruch's language from "only for her" to "also about her."

That's an approach that I've heard from many contemporary marital educators: in a healthy relationship, it can't be *entirely* about only one person.