Many sources count the Amazon river as the river with the most tributaries. There are thirteen major tributaries (IE thirteen other places that give the most water to the Amazon river), but there are estimated to be over 1,100 tributaries in total that feed into the Amazon river in some way. That’s a lot of water to flow into the river, which is why it’s the largest river in the world.
As the previous answer noted, it’s hard to get a full answer to this question. There are lots of ways to get water from one piece of land to another through channels and things on the land and under it, so it’s hard to count exactly how many tributaries are feeding the Amazon. Accessibility is just one issue out of many, though.
The Amazon has 1,100 tributaries, probably the most; the Mississippi has only four; the Nile, only two while the Ohio has around 65 and the Thames, similarly. India is often called the land of rivers, the Ganges and the Indus serving the fertility of many countries.
Having said this, there may well be tiny tributaries that have not been counted if they are in remote areas. It's probably a good idea to remember the Amazon as having the most tributaries in the world.