The current maximum is 3000 for Pokémon storage, and 2500 for item storage.
Originally, it was 1000. As others have also, I fully upgraded mine. I can also confirm that the price stayed the the same for every upgrade purchased to the maximum.
Here is a screenshot of my storage at 1000 each, and the message I got after trying to buy another upgrade once the cap was reached:
Is it worth maxing Pokemon storage? It really does come down to this: for most people, this is NOT necessary. It simply fits the way I wanted to play Pokémon GO. I am not interested in having the highest CP Pokémon or battling Gyms for the time being. I simply enjoy playing "my way", I don't see the value of maxing out Pokémon Storage for 99.999% of players.
Updates:
- In June 2017, max capacity for items was increased to 1500.
- In May 2018, max capacity for items was increased to 2000.
- In July 2019, max capacity for Pokemon was increased to 2500.
- In November 2019, max capacity was increased to 3000 for Pokémon and 2500 for items.