Free?
Obviously not the best way to make money, but a good way to get your name out there, and earn some good karma points while you're at it.
Advantages: maximum exposure to users, everyone who might possible have a use for it considers a free app and will probably install your app even temporarily. You get an opportunity to impress them and build a trusted name with them. The Android Market also lists other apps by the same developer, so viewers of your free apps on the market will be exposed to anything else you publish, driving traffic towards any other apps you might have.
Disadvantages: Without charging for the app itself, you have to use advertising or in-app purchases or other tie-ins in order to make money (see next).
Free with Ads?
Advantages: Ad providers such as admob support house ads, which is advertising for your own products. This opens another opportunity to use your free apps to drive traffic towards any paid apps you might have, or other free offerings too.
Disadvantages:
Advertising sdk's usually add an additional weight to your app size, and there's the obvious loss of screen real-estate also. Additionally, people have to actually use your app in order to see and hopefully click on the ads, so unless your app involves a decent amount of user interaction this might not be for you. To make the most of advertising you want to have an app that keeps users coming back to the screen. Something like a countdown timer for instance might not be so suitable for an advertising-based revenue model as the concept involves minimum user face time, users typically set the timer and turn off the screen.
Advertising platforms:
Free with in-app purchases?
Advantages: You get users in the door and using your app, now you can ply them with the ability to purchase additional related goods in-app. Micro-payment systems mean that your users have the option of adding custom content for mere cents, all within the bounds of your free app, and an app that might not generate much interest even at the lowest price point (usually 99c), is able to still generate income. You get the user mass by distributing your core app for free, and then can utilise novelty-driven or premium-functionality requirements towards generating income. Can also be combined with Advertising, but be mindful of how this can adversely affect user perception of your app.
Disadvantages: more complex to implement that advertising, and obviously requires actual additional content which not all apps are suited to. Micropayment systems not available in all countries.
In-app billing/virtual goods/virtual currencies:
Free cut-down or trial version and paid 'pro' version?
Advantages: Similar to in-app purchases and other 'freemium' techniques, you introduce the users to the concept of your app in the free version, then hope that some of these users are willing to pay for additional content once your free version has earned their respect.
Disadvantages: Unlike in-app purchases and the micro-payment model, the paid 'pro' version is restricted by the minimum price point of the market through which you're distributing your app which in the case of the Android Market is 99c. If you don't have the additional content to warrant meeting that initial price threshold, you're flat out of luck.
Paid?
Advantages: You make profit upfront, regardless of how much someone uses your app, and regardless of even if they keep it installed. Once they've past that initial 15 minutes to refund, you profit.
Disadvantages: Android users are a notoriously stingy bunch, although as more Android users could be considered the mainstream demographic rather than the tech-head early adopters, this may change. Piracy can also be an issue, so make use of the licensing validation library provided by Google. Paid apps also run the risk of being undersold by a competing free product that relies on one of the other methods above to generate income. Also, as strange as it might seem, many users balk when confronted with the option of paying 99c for an app for their $500 device.