Mud wise there is frandomm, which is entirely quest based, alteraeon and cyber assault which both have lots of quests, plus 4dimensions and newmoon, though puzzles can be hard in those games.
Browser rpgs are harder to find but there are some on the ground. Puppet nightmares is entirely story based, with a very complex battle system (though also a complex interface to go with it), Drakor has lots of quests though it'll take you some time to complete them, and of course there is always good old kingdom of loathing or twilight heroes, though the last two are a little more random in terms of solutions etc.
Graille lords is a game lots of people are liking so far, but how that is on the questing currently I do not know as I've yet to try it seriously.
In terms of other text rpgs though, there are always soem great single player options, especially on Ios like path of adventure and of course gamebooks with many multiple paths.
With our dreaming and singing, Ceaseless and sorrowless we! The glory about us clinging Of the glorious futures we see,
Our souls with high music ringing; O men! It must ever be
That we dwell in our dreaming and singing, A little apart from ye. (Arthur O'Shaughnessy 1873.)