Since Islamic definition of self-denial is somewhat different from some other religions, let me first write a bit about its meaning in Islam.
Self-denial in Islam is called zuhd. Literally, zuhd means getting a sufficient and as little as possible amount of something. It is the opposite of being greedy and insatiable. As a word in Islam, it means preventing your spirit from paying excessive attention to everything except God. It doesn't mean not seeking a good worldly life, but rather not paying attention to it. It means being able to abandon everything you have in your life at will for God and not depending on them. So it doesn't contradict being wealthy or wearing decent attire; quite conversely it encourages people to have a good worldly life while being able to prevent themselves from being a slave of their properties. In other terms, it is said by the first Imam of Shia Muslims, Imam Ali that (a hadith): "Who does not become very happy with what he gets and does not become sad when loses something is zahed (has zuhd)". (Sorry for my bad translation, it was the best I came up with!).
Also, zuhd has some stages. The first is preventing yourself from indulgence in mundane life, and ultimately it means not paying attention to anything in life and afterlife, but God.
Now let me point to some of the instances in Quran about self-denial:
And whatever thing you [people] have been given - it is [only for] the
enjoyment of worldly life and its adornment. And what is with Allah is
better and more lasting; so will you not use reason?
Indeed, We have made that which is on the earth adornment for it that
We may test them [as to] which of them is best in deed.
Wealth and children are [but] adornment of the worldly life. But the
enduring good deeds are better to your Lord for reward and better for
And the worldly life is not but amusement and diversion; but the home
of the Hereafter is best for those who fear Allah. Do you then not
No disaster strikes upon the earth or among yourselves except that it
is in a register before We bring it into being - indeed that, for
Allah , is easy -
In order that you not despair over what has eluded you and not exult
[in pride] over what He has given you. And Allah does not like
everyone self-deluded and boastful -
The Day when there will not benefit [anyone] wealth or children.
But only one who comes to Allah with a sound heart."
So as for he who transgressed
And preferred the life of the world,
Then indeed, Hellfire will be [his] refuge.
But as for he who feared the position of his Lord and prevented the
soul from [unlawful] inclination,
Then indeed, Paradise will be [his] refuge.
There are many other instances that I may add later. Hope it helps!