Alexander stopped his Indian campaign at the Ganges because his soldiers mutinied and refused to go any further. There are many reasons given for this. For one, they were very far from home and had been on campaign for a very long time. Secondly, the Ganges was quite wide and deep and there was a large Indian army waiting for them on the other side.
As for the Mongols, at the height of the Mongol Empire, the mongols did occupy Kashmir and the Punjab. However, they were unable to defeat the Delhi Sultanate, so they couldn't push further into the subcontinent. You could argue, however, that the Mongols did eventually conquer India, as Babur, the founder of the Mughal Empire was a descendant of Genghis Khan.
hi! re the Mongols, you'll find more information in this post from the FAQ: