Sometimes 2 + 2 = 22 is just what the doctor ordered. (just don't bring it up in math class)
Consider this as the flip side of the coin from yesterday. Even though I don't think simplicity is bad doesn't mean that I think complexity is the devil either; it's just something that's a little harder to pin down, and I'd also say something that's more difficult to use properly as well.
There are many different kinds of complexity, for example a game can have a complex story or plot like a lot of JRPGs - love it or loathe it one thing that everyone can agree on is that Xenogears had a really complex story, again, whether or not this is a good thing is up for debate. A game can also have complex controls, I invite you to look at the controller for Steel Battalion in all its glory. Complexity can come across through gameplay as well, whether in terms of learning curve or difficulty or depth of play. Any game can be complex in many ways, sometimes more than one.
I think the ultimate question though, as with simplicity, is when should complexity be used?
This is where it becomes a bit of a different beast from simplicity. As reason dictates, the more complex something is, the more potential points it has where failure can occur. Simplicity is not without risk, certainly, but I don't think that I'm going too far off base to say that it carries less of a risk than being overly complex. Complexity is often divisive in nature, as I hinted at above: some people love complex stories, controls, or gameplay while other people could either care less or are outright turned off. That Steel Battalion controller is a complete monster and also had a hefty price-tag on it. While such a device does allow for a good deal of immersion, it also can prove to be frustrating to someone that merely wants to hop in and play a game, not buckle down into a cockpit for a mech simulator.
It's a fine line to walk, between complex and simple. I think that a game that does it particularly well is the first Portal. Portalling in and of itself is a somewhat complex mechanic when you think about it, this in addition to being something that wasn't really seen before. The game does a good job of familiarizing you with the mechanic though before sending you on any really difficult tasks. The complexity is somewhat of a departure from the norm, but not so much that it's difficult to understand and work through.
On the other end of the spectrum is my favourite thing in the whole wide world (if any sarcasm detectors are active in your area they've just exploded): motion controls. The best -- or would that be worst? -- example I can think of is Lair, a game which had a lot of promise and a decent premise, but the controls that focused on the sixaxis aspect of the Playstation 3 design just turned the thing into a clunky mess; even the more traditional controls that were implemented later didn't really help matters much. Here complexity hurt a game a lot more than it helped it.
Basically if there's one lesson to learn it's that both complexity and simplicity are tools that must be used correctly. Neither of them are there simply for the sake of being there, and there are times when one will be more suited to a particular task than the other. Figuring out when to use which is something that separates great game design from merely mediocre efforts.