My laptop uses a charger outputting 6.4A with 19V (120W). This charger was a replacement for the old one, the specs were almost completely matching (19.5V and 6.15A on the old charger), everything works perfectly.
There is, however, another laptop, which doesn't see the charger when working and barely charges with the 20V and 2A of the AC adapter, which is 40W. It sounded like a clear indication of not enough Amps, so I checked that the voltage and connector were (almost) matching and tried it with my adapter (3 times more powerful), and it worked perfectly.
I have heard before that it is completely safe to bring more Amps, because amperage is pulled, not pushed, so I believed the experiment to be safe, and was going to buy the same charger for the laptop's owner -- but she has also asked her brother, and her brother told that it is not safe to change amperage by more than 2A, some googling revealed the same statement about 1.5A. So I would need to find out the original amperage and choose a charger carefully.
So: Is it completely safe to use a charger with considerably bigger amperage if other specs, including polarity and connector shape, are matching? Is there any limit to this?