King of the Sandbox said:
Pokemon trainers (immense options for team building) and Final Fantasy 7 (the Materia system) come to mind for some highly customizable characters. It's true that their story is rarely customizable, but that's not the only way to make a character your own.
And you get a grand total of two sword upgrades (one optional), one hookshot upgrade, and some bigger pockets in Ocarina of Time. Link to the Past didn't even have that much. Actually, many games give you upgrades...power-ups in Mario, better guns in Duke Nukem, ect. Too many games upgrade your weapons to count that as belonging to RPGs alone. RPGs use better gear to upgrade your character(s)'s stats, like Final Fantasy, or World of Warcraft.
And dialogue and story are hardly RPG elements...they're not even exclusive to games. Silent protagonists don't qualify either because they dominated gaming in its early years; Frogger, Pac-man, Mario, Mega Man, Simon Belmont, Sonic, and the pong paddle are all mute in their game debuts. As for Link's punny name...take a look at Miis. They are nameable and customizable. Would you consider Wii Sports to be an RPG?
Many RPGs give you high levels of customizable options. Some offer CYOA-style influence on the story. However, the core of the RPG, the one thing connecting everything from Wild Arms to World of Warcraft, is the numbers. The Legends of Zelda (well...all except Zelda 2) do not have stats deciding if you hit, how much damage you do, encounter rate, ect. The only RPG element I can think of is drop chance of Rupees while cutting grass or ramming head first into trees (actually, I'm not even sure if this is random), and that is just too mild to call it an Adventure-RPG hybrid. It's not an RPG.