Who will verify any transaction when the upper bound to total number of bitcoins is reached? I've read that there will be around 21 million BTCs. (How many bitcoins will there eventually be?)

Also, to my beginner understanding, it seems that miners verify the active transactions. (What are bitcoin miners really solving?)

To my understanding this means that if the upper bound of 21 million bitcoins is reached, no new transactions can be made, because noone will verify them. But this would render the already available bitcoins useless... Am I wrong? How?
Please see here https://en.bitcoin.it/wiki/Transaction_fees .


  It is envisioned that over time the cumulative effect of collecting transaction fees will allow somebody creating new blocks to "earn" more bitcoins than will be mined from new bitcoins created by the new block itself. This is also an incentive to keep trying to create new blocks even if the value of the newly created block from the mining activity is zero in the far future.