I would only want puzzles where it made sense to have them. A dungeon where areas are guarded by a puzzle that only those that are supposed to be in there are supposed to know the answer... and so yes, I'd want it mandatory for continuing into the dungeon areas ~protected by the puzzle.
Other places might have a puzzle that wasn't really meant to be one, but has become so... like a sewer with levers that open and close passages (that were once filled with water, and the levers behavior well known to the operators ~but not to the PC; hundreds of years later).
Others could just be some wild whim of an NPC
*** One thing though...
With the advent of mass internet, puzzles with fixed answers are rendered pointless. What needs to be done, is to have the game generate solutions, or changing the path to the answer; on a per game basis (and not just picking from three paths or so). This would discourage (and /or make difficult) having a common solutions list being passed around on the web.
Oblivion actually went some way to add puzzles to certain areas, it was good for that.
Unfortunately it was quite rare.
The imperial sewers had a mini pully puzzle to raise grates up or down to allow or deny access to areas.
There was a dungeon above Chorral that had hidden access to to an area with a unique encounter that was easy to miss.
One mage guild quest had a large ward guarding an area that relied on a series of spell effects being cast in order to open.
A ew other ares had hidden access or ambush sites.
Some had a maze effect where going one way would allow you to go around others.
It was very well handled for the game style.
However I hope more effort is to placed in this for Skyrim.
It does not have to be in every area but a large percentage of areas would be nice.
As for riddles, I hope they have some aslo.