In my opinion, both the idea and it's execution are equally important.
Execution is what gives physical form to an idea. Yes, an idea. Without an idea first, any execution, if existing, is completely worthless and pointless.
If you pay attention, many of the answers here are actually labeling the good execution of good ideas as just "good execution (of possibly nothingness)".
I'll use a different perspective on the Infinite Monkey Theorem here: Execution without ideas is like you having an infinite amount of monkeys randomly typing text, but without any idea of what to do. Chances are they will give you a centillion (10^303) worthless papers before you get your first "William Shakespeare's work".
You can make the most advanced, reliable, visually appealing chess game ever made; You will still not rise much higher than any other professional chess game currently on market. The reason is, even tough the execution could hardly be any better, the project's goal, the idea, is terrible if you consider how many professional chess games are out there and how much the execution costs compare to those.
Much like execution is nonexistent (or otherwise waste of resources) without an idea behind it, ideas that are never executed are also worthless; If they never turn real, they are a waste of thought and time.
Execution is what gives physical form to any idea. In a sense, the execution is an idea's body. Some people will hate me for giving this example in this way, but, an idea without a good execution is like Stephen Hawking: "Brilliant indeed, but still looks retarded."
Finally, in today's market for games or whatever software really, you will need both to be good in order to be successful. Too many people in too many places have too many ideas and/or too much time and money to work on them. And finding something that has not yet been done (and done well), although still not too hard, is not a simple task.
[Additional section] The devil's lawyer (Idea's defense):
I don't know if this is true for all successful games, but every single successful game I know about has an excellent idea behind it!
Many fellow answers here give examples of "why execution is far more important than the ideas behind them", that are missing a very important point:
There is a difference between general-concept ideas, and ideas for distinctive characteristics.
Most (if not every) successful games have distinctive characteristics that make them essentially different from other games of the same genre.
For example, even tough many FPS games have the same "soldier in WW2" concept, successful ones that do not have a distinctive characteristic are extremely rare, in case any even exists.
The idea that makes a game successful is usually not that of it's top-level general-concept, but those of it's characteristics and smaller concepts that make it different.
Take the multi-player gameplay of Counter-Strike: Source and Call Of Duty: Modern Warfare (1), for example; Both of them are First-Person-Shooters of quite the classic essentials; They are not very different from a shooter's perspective.
Essentially, you have modern guns, a scenario to use, and enemies to shoot, in both games. But can you call them the same? Far from that, right? Well, take graphics, physics and even sound out of the equation; Are they still different? Sure are, aren't they? So here is the golden question: What exactly makes them actually different to the players?
Well, the answer to that is: "Mostly, the way you acquire your weapons, and the way you respawn".
- In CS:S, weapons are acquired per-match with currency acquired
per-round; and spawning is round-based (obeys a "hardcore" style), and dying in a
round means you will only re-spawn at the start of the next.
- In COD:MW, weapons are player-based and unlocked to player's
accounts as they gain experience points and advance in "ranks"; Spawn
depends on match mode, but is, on the default game mode of "Team
Deathmatch", only delayed for 15 seconds.
The top-level concept of both games is practically the same, and both games have good execution, but the ideas that brought the different characteristics plays a critical role in both's successes, as otherwise, with similar concept, characteristics and execution, either the older would be abandoned in favor of the newer, or the newer wouldn't be popularized because the older exists.
Thus, good ideas are critical to a game's success.
And good execution, to successfully implement those ideas, is also critical.