Fish require dissolved oxygen (which isn't the same as "air", per se).
With adequate surface agitation to create gas exchange (provided by something as simple as the exiting outflow of water from a hang on back filter, return flow from a canister filter, etc), no additional 'aeration' devices, or bubblers are required.
Powerheads and other non-aeration water flow devices agitating the water surface work as well.
Example:
