You will find a huge selection of task management or to-do list apps for Android. Many will have similar features and prices so my recommendation is to give them a try and find the one that meets your needs and preferences. I have tried a few different ones and have listed some of them here.
Task List (Free)
Setting up tasks or a list of tasks in Taskos To Do List is relatively straightforward. When you start the app, you are immediately presented with your current list of tasks. The apps are listed in order of priority but you can easily sort them by date or category. When creating a new task, you will be given the option to add priority, category, date due, if you want to share it with contacts, and an alert or alarm for the task. Voice input is also available.
Taskos To Do List will sync with your Google Tasks. To remove a completed task you simply swipe across the screen and then shake your phone. The app comes with a couple of widget options for your home screen. The user interface is bright and not very cluttered. There are plans to have the app sync with services such as Remember the Milk, Producteev, and more in the future.
Any.DO To Do List & Task List (Free)
Creating a task or list of tasks in Any.DO To Do List is very quick. When you type your task items, the app has word prediction built in to help you out. There is also voice input. When you first start the app, you will be given a list of current tasks based on date. When adding a new task, you can assign the priority, folder (or category), reminder (alert), notes or extra details, and finally the ability to share it with your contacts.
The user interface for Any.DO To Do List is nicely done. The font style and size are very easy to read, and you can choose between a light or dark theme. When sharing tasks with others, you will get a notification when the task is updated. The app syncs with Google Tasks and has four different widget sizes. Future updates planned will allow the app to sync with gTasks, RTM, Producteev, Springpad, and others. Maybe the most useful feature planned is a web interface.
Producteev by Jive (Free)
Producteev is a web-based task management service that has been out for some time, but they only recently launched this Android app. Since its initial release, it has undergone a number of updates and works well with its website. Producteev is appropriate for individual or team use. Within Producteev, you can setup workspaces and then within those workspaces organize tasks by labels. For each task you can assign a priority, due date, and share with team members.
Producteev is probably one of the more detailed or complex task management services, since it is coming from a web based service. The app will allow you to filter your tasks by seven different components. The app only has two different widget sizes for the home screen. The app works offline and syncs in the background with Producteev. If you want/need a web interface for your task or to do lists, Producteev is an excellent option.