Is it permissible to sell autographs of famous people?

Firstly: 

In order for a sale to be valid, the fuqaha’ have stipulated that the sold item should be something beneficial. It something is of no benefit, it is not valid to sell it, because it has no value, as there is no benefit in it; his taking money for it comes under the heading of consuming wealth unlawfully. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 

Selling that in which there is no benefit is not permissible. 

End quote from Majmoo‘ al-Fataawa, 31/224 

Ibn Qudaamah (may Allah have mercy on him) said in al-Mughni (4/174): 

It is not permissible to sell that in which there is no benefit. End quote. 

It says in al-Mawsoo‘ah al-Fiqhiyyah (29/148): 

The fuqaha’ are of the view that it is permissible to sell birds whose flesh may be eaten, such as pigeons, small birds and so on, because there is some benefit in it. As for selling birds that are not eaten or used for hunting, such as Egyptian vultures, kites, ostriches and crows, that are not eaten, it is not permissible to sell them, because there is no benefit in them and they are of no value, so taking money for them comes under the heading of consuming wealth unlawfully and spending money on them is foolishness. End quote. 

An-Nawawi (may Allah have mercy on him) said: Our companions said: It is permissible to sell books of hadeeth, fiqh, Arabic language, literature, permissible poetry that is of benefit, books of medicine and mathematics and so on, in which there is some permissible benefit. Our companions said: and it is not permissible to sell books of kufr because there is no permissible benefit in them; rather they must be destroyed. The same applies to books of astrology, magic, philosophy and other kinds of forbidden and false knowledge, and selling them is invalid because there is no permissible benefit in them. End quote from al-Majmoo‘, 9/304 

What is meant by value that is connected to the benefit is the monetary value of the sold item. 

It says in Kashshaaf al-Qinaa‘ (3/152): 

The third condition is that the item sold and the price paid should be wealth, because it is being exchanged for wealth, as a sale is the exchange of wealth for wealth. And this wealth, according to the shar‘i definition of wealth, is “that in which there is a permissible benefit, without that resulting from need or necessity”. That excludes that in which there is no benefit at all, such as insects; that in which there is a haraam benefit, such as alcohol; that in which there is a permissible benefits because of need, such as a dog; and that in which there is a benefit that becomes permissible because of necessity, such as dead meat (which was not slaughtered properly) in the case of one who is starving and alcohol to wash down food that is stuck in the throat (if nothing else is available).

End quote. See ash-Sharh al-Mumti‘, 11/6 

Thus it is known that if something is of no benefit and it has no monetary value, it is not permissible to buy or sell it. 

That includes the autographs mentioned, because there is no benefit in them and they have no monetary value. So it is not permissible to buy or sell them. 

Secondly: 

It is well known that trading in such things is not usually done, except in circles that have gone astray from the etiquette and rulings of sharee‘ah, such as among artists, sports stars, media personalities and the like. These are people whom it is not befitting for the Muslim to follow or emulate, even if there does not seem to be anything that is contrary to Islam in their private lives. Rather what is prescribed for the Muslim, and the proper etiquette in his case, is to focus his inclination on emulating good and righteous people, because whoever imitates a people is one of them. 

Moreover, if the one who buys such a thing is asked on the Day of Resurrection about his wealth and on what he spent it, what do you think his answer will be on that Day? 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

One of the bad deeds is wasting one’s money which Allah has made a means of support for people, by means of which their well being is maintained in both spiritual and worldly terms. Wasting money is spending it on that in which there is no benefit or that which is harmful. 

End quote from Fataawa Islamiyyah, 4/497 

As for the one who sells it for a large amount of money, as usually happens, when he is asked on the Day of Resurrection: on what basis did you allow yourself to take your brother’s wealth, and what did you sell him in order to take his money, how will he respond?! 

See also the answer to question no. 40752 

And Allah knows best.