You can normally adjust from the non-drive side.
I've done this on standard Shimano cup/cone hubs as well as various Mavic hubs and Formula sealed bearing hubs.
As recordace says, there are some differences. Some need a small allen key to adjust the bearings, some just cone spanners.
Most of my wheels have only needed cone spanners to adjust the bearings (cassette or cup/cone) - I only have one set that needs allen keys (but they have never needed to be touched)