Freemium or free-to-play have been the business model buzzwords in games for the last two years. We've begun to move from the kneejerk reactions ("they're not even games", "people who play them are stupid") to an emerging acceptance that freemium games are a viable business that can also support fun, engaging games.
I remain a huge supporter of free. I believe that free is the natural price point on any platform where the price of making one more copy is as close to zero as makes no odds. There are some situations where I believe paid may, possibly, be a better solution:
If you have a strong brand: the primary advantage of free is that people who don't know your IP, brand, or game can experience it easily. If you already have a strong brand, you may be able to price high. (Few brands are actually this strong)
If you are a marketing-led organisation: If marketing is your USP as a business, you know how to persuade gamers to part with their money for a game. It might be worth playing to your strengths.
If your product is the best game the world has ever seen: this is highly unlikely
In essence, you will have to spend money to market your game; the higher the barrier to entry (i.e. the price), the more likely you are to have to spend lots of money to market your game. So in most cases, I would argue in favor for free.
But whether I am arguing for free or not, I always support allowing users to spend more money in the course of their enjoyment of the game.
The internet has enabled you to find your biggest fans and let them spend more money with you. Whether your game is free or paid-for, it will have cost you money to acquire customers. Some of those customers will love what you do. How will you enable these fans to spend lots of money from you?
The screenshot of Infinity Blade's iTunes page shows you the top in-app purchases for the game. The most popular upgrade (for a game that sells for £3.99) is £2.99. They also sell IAP for much higher rates, and in total IAP, is about half their revenue.
I believe that games should go free, or they should go expensive. Never be cheap. But always, always, always offer IAP.