Aragorn did more than touch the stone in the book - he wrests it to his own mastery, and sees things in it which are crucial for the plot. But as with so many things, it didn't happen as shown in the movie.
When they return to Helm's Deep after the events at Isengard, Aragorn appears looking grey and has this conversation with Legolas and Gimli:
'I have looked in the Stone of Orthanc, my friends.'
'You have looked in that accursed stone of wizardry!' exclaimed Gimli with fear and astonishment in his face. 'Did you say aught to - him? Even Gandalf feared that encounter.'
'You forget to whom you speak,' said Aragorn sternly, and his eyes glinted. 'What do you fear that I should say to him? Did I not openly proclaim my title before the doors of Edoras? Nay, Gimli, I am the lawful master of the Stone, and I had both the right and the strength to use it, or so I judged. The right cannot be doubted. The strength was enough - barely.'
He goes on to describe how he hopes that revealing himself to Sauron would cause him to act more hastily and launch his attack before he is fully ready. And, one of the things that Aragorn sees in the stone is the Corsairs fleet sailing up the river, ready to attack from the south - which is the trigger for the crucial ride through the Paths of the Dead, which IIRC was missed out in the movie altogether.