What happens when Bitcoin mining no longer yields new coins?

https://en.bitcoin.it/wiki/Mining

Mining is the process of adding transaction records to Bitcoin's public ledger of past transactions. This ledger of past transactions is called the block chain as it is a chain of blocks. The block chain serves to confirm transactions to the rest of the network as having taken place. Bitcoin nodes use the block chain to distinguish legitimate Bitcoin transactions from attempts to re-spend coins that have already been spent elsewhere.

The current incentive for helping validate the block chain is a mining reward. This is an award given for discovering a block. However, the total number of Bitcoins cannot exceed 21 million, so this reward will taper off. But there is also a fee mechanism:

Additionally, the miner is awarded the fees paid by users sending transactions. The fee is an incentive for the miner to include the transaction in their block. In the future, as the number of new bitcoins miners are allowed to create in each block dwindles, the fees will make up a much more important percentage of mining income.

This suggests that fees will become the new incentive for "miners" (who at this point are no longer "mining" new coins, but rather just validating transactions in exchange for the fee). What will this fee become at 21 million coins, such that those validating the block chain have an incentive to do so?

Moreover, what institutions could take advantage of validating the block chain, if fees were low enough that it were not profitable?