Uses sprites much like older PC RPGs (such as the early Ultima games), in that characters did not face in a particular direction, but instead always face forward.
When you want to talk to someone, you have to choose a direction first.
NES Version
Battery-backed SRAM system.
Dragon Warrior release was allocated more memory for graphics improvements
Characters were given directional appearance and was also applied to all moving NPCs.
Coastline graphics were slightly upgraded to appear better.
When you want to talk to someone, the direction you face is used. This also applies to all moving NPCs as well.
SFC Version
Hero is able to carry multiple weapon and armor items. Previously, only 1 of each type of equipment could be held.
Experience and gold given by monsters is increased.
The dragon guarding the princess is given an on screen sprite.
Shrines are given world map sprites rather than simply staircase sprites.
Shrines are given a unique soundtrack. The same music which is used for shrines in Dragon Quest II.
The Silver Harp will summon any enemy in the area when used, as opposed to the NES Version which would only summon monsters from around Tantegal or the Mountain Cave.
Roto's Tablet is now a tombstone that appears in place of the chest containing it.
GBC Version
Many names in the game have been shortened due to GBC's display constraints.
Addendum
Name alteration: Dragon Quest is the original name. It was launched under that name in Japan. The North American release came across some trademark issues over that name, and as a result; began as Dragon Warrior.
Dragon Quest has the logo on a solid-color background Japan Release / Trademark free logo
Dragon Warrior has a more generic logo on a somewhat more interesting background North America Release / Compare this... It also moves all the options to menus following the title screen.
At some point shortly after its launch in North America, someone with infinite wisdom noticed that there were some issues/typos with the translated copy, and so came the birth of a second version To this. And... PRG0... When it looks good on paper to PRG1...See? Infinite wisdom
Some townspeople sprites from the Japanese version are present in the monster graphics of Dragon Warrior, unused.
The locations of "SEARCH" and "DOOR" {しらべる and とびら, respectively} in the control menu, were switched out due to the longer English text.