BillsReminder, a bill-tracking app, isn't free--but it does offer a 30-day trial version, which provides you exactly enough time to try it once. Unfortunately, although it does a lot of things right, it has some frustrating and nonintuitive aspects to its design.
I'll start with what BillsReminder does well. Setting up bills is easy and straightforward: You enter the payee, the amount, the category (household, utilities, taxes, and so on), the due date, any notes associated with it, and the number of days before it is due (to set a reminder). You have the option to set up a bill as recurring, a useful feature for rent and other fixed monthly expenses. The app also allows you to take a picture to associate with a particular bill, a feature that completely baffles me--I honestly cannot say why anyone would need or want to do this. If you prefer, you can set up income as opposed to bills, so you can use the app as a way to balance your checkbook, as well.
The main screen lists bills in chronological order, from the one that is due soonest to the one furthest away. The list includes the date each bill is due, the number of days until it is due, and the amount owed. In the top-right corner you can see the total amount due. From the settings you can change the default for triggering a reminder based on how many days before the bill is due, as well as the reminder time. You can also set the currency that BillsReminder uses, and manage the bill categories in a variety of ways (such as associating them with colors or establishing parent categories). You may create new categories if you have expenses that are not featured.
The biggest problem I have with BillsReminder is that paying or removing a bill requires you to click on the bill to go to the bill screen to deal with it. That's an extra step I would prefer not to take, and it becomes tedious if I have to juggle lots of bills and expenses. Being able to select multiple bills at once would be much better. On top of that, in my tests the app crashed fairly frequently. If this app were free, such flaws would be easily forgivable; I am reluctant to pay for such inconsistent service.
If BillsReminder isn't quite what you are looking for, consider the more robust Mint.com Personal Finance app for Android phones.
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