The goal of the Three Heart Challenge is to complete a Zelda game without picking up any Heart Containers or collecting enough Heart Pieces to form a new heart container. Hence, all the Heart Containers you'll get are the original three (in most games) you start out with. This is able to be done in twelve of the fourteen Zelda games. The exceptions are Four Swords and Four Swords Adventure for obvious reasons, and Link's Awakening and Link to the Past, since you are have to collect the Heart Containers dropped by bosses to continue.
Legend of Zelda[]
Difficult, but possible!
Adventure of Link[]
In order to do the Three Heart Challenge in Adventure of Link, just never upgrade your Life stat.
Ocarina of Time[]
Very basic to do. Probably one of the most completed Three Heart Challenges.
Majora's Mask[]
Hard, but not impossible.
Oracle of Ages[]
Possible but quite difficult.
Oracle of Seasons[]
Possible but extremely difficult. This is most likely the hardest that allows this challenge. You have to be an very seasoned Zelda player who takes on these type of challenges with ease in most or extremely gifted to do this.
Wind Waker[]
Simple to moderate to complete. The parry feature allows for most attacks to be countered without enduring any health damage. The player will have to obtain the heart piece map before pulling treasures out of the ocean.
Minish Cap[]
Fairly difficult, however the real challenge in this run is the final boss. You'll have to strategize much more carefully there than what's thrown at you every other dungeon.
Twilight Princess[]
Can be completed with moderate difficulty. Player will have to skip some side quests to avoid being rewarded with heart pieces.
Phantom Hourglass[]
Spirit Tracks[]
Again, pretty basic.
Skyward Sword[]
For Skyward Sword, the same rules apply. However, it is more like a Six Heart Challenge since you start off with six Heart Containers, instead of the traditional three.