I am a school teacher (hence why font is comic sans), and nothing makes me more enthusiastic than a good game that encourages thinking, and I don't mean calculating the best item to pull of a critical 23% of the time while increasing armour to resist fire 98%. I mean serious strategical thinking that alters as you play due to constantly changing through unpredictable situations. Let me explain in more detail.
Many MMOs focus on the concept of pick a class/race then outfit with specific items to get the best out of your character dependent on their role in the game. If I were a tank class, for example, then I would be expected to get items that increase my protective skills or rolls. If I were to be the same tank class and yet get items to increase my damage then I would generally get other players either criticizing or not grouping with me because most likely I have no idea how to play my character. As a result I am defined by the game mechanics and design and am not putting effort into determining new strategies for how to play a class outside of its box.
Take now an example of a game where you select your class but you can select skills to step away from the normal. Lets say I choose a Tank but this time select skills related to ranged dps. I then become a ranged dps who hits less (due to my class stats) but lasts much longer. My strategies would reflect this by my ability to stand ground for longer, resist attacks from opposing ranged dps (and not hide), and pester, but not kill as fast, other dps. My thinking and adaptability is showing itself.
I am now going to use an example from my past experience in World of Warcraft: Burning Crusade (I stopped playing in 2008). My main character was a warlock and as such I was a definite dps. At the time most warlocks chose heavy destruction (fire) mixed with shadow skills in order to increase their dps. If you did not do such then you often got criticized in large raid for not pulling your weight. I was criticized for a while with my skills because I did not choose such skills... until they realized I actually had a larger damage over the whole dungeon. Why? Because my skills let me live longer... thereby letting me do more damage over time. I was so good at staying alive I often successfully off tanked in emergencies.
This is common in many games where people rely on not thinking about their strategy and their class.
Now WoW might have been a bad example as it is rather predictable, so I will move to a game where altering situations is more dominant, specifically Warhammer Online. I am choosing Warhammer as an example, there are better ones, but their situations are often more complex, so I am attempting to stick simple.
Warhammer Online has the common task of fighting the opposing player side in PvP (or RvR for pedantic people). Because different castles are taken by different sized groups, players are often forced to send out scouting parties and attack specific holdings to maintain superiority. there is often a give-take relationship where a war band will be forced to let the enemy take some land in order to take another piece of land. As well as this there is the constant shifting of numbers as people log in and out of the game, where once you my have had the upper hand you no longer do, therefore need to focus on getting a defensible position before you are overpowered. This constantly shifting position is the concept of strategy and thought where knowledge and wisdom take charge as opposed to mathematics and predictability and is more common in PvP games (although not always present).
So why choose a game that requires you to think about what you do?
The most important aspect to thought in an MMO is that it provides more of a feeling of having done something. Using the mind encourages you to feel like you have participated and are not just standing there to make sure the others have full hit points (yes, healing can be boring sometimes).
A second aspect is to teach you things, this is the same concept as the game of chess. By participating in a thinking MMO your mind is constantly learning about how people behave, how actions have consequences and thinking ahead (predictable instances rarely let you think further than the current monster).
The final aspect is that a thinking MMO encourages teamwork. By teamwork I do not mean "I tank, you heal", I mean your ability to adapt to the situation based upon how your team-mates work.
Remember: Chess is 3D, why can't an MMO require thought?