Exploration, items that you use intelligently to advance, and ingenious puzzles are all staples of the Zelda series (as is a high level of polish). The original Zelda (personally my favorite game ever) was just so far ahead of its time for its day; there was nothing like it on consoles. What made Ocarina of Time so special for me (besides the end sequence) was the fact that they successfully managed to take Zelda's creative puzzles and implement them into a 3D world.
Zelda games often make you ponder your situation based on your current abilities and the items at your disposal; they make you think to a degree, which is very rewarding when you finally figure out what to do.
These examples, plus the fact that all combat is real-time and fun, propels Zelda as a franchise to being my favorite series of all time. It is often imitated but never quite duplicated.
