Although, you can do android development using any programmer's text editor along with the tools provided by Android SDK; an Integrated Development Environment (IDE) helps to build faster and better code in less amount of time.
Features of an IDE in the modern world:
1) Source code editor
2) Integrated Compiler / Interpreter
3) Debugger
4) Build Automation Tools (after all we developers are lazy)
5) UI Designer
6) Version Control
7) Auto Complete
and many more.
Available IDEs for Android:
1) Eclipse with ADT: Eclipse is an open source IDE freely available for download and development. It is easily extensible to support many other features, languages and tools. One of the plugin for Android comes from the house of Google named Android Developer Tools (ADT). By installing this plugin in Eclipse, you get Android template projects, Android UI designer supporting drag-and-drop functionality, many other features. It is also officially supported by Google.
2) Motodev Studio For Android: It is an extended version of Eclipse built by Motorola company which moves one step forward compared to Eclipse. In Eclipse, you have to download all the plugins manually while in Motodev Studio For Android, that strain has been taken away from you. You have to install it and start developing your android applications. It features inbuilt ADT, access to Motorola APIs, Motorola emulators, Code Snippets, App Validator, App Signing, App Deployment, Database Management, Emulator Screen Capture, Develop with C / C++ for high performance apps. You have to register first to download the studio. Registration is free.
3) Google App Inventor: An online development tool from Google Labs. You have to sign in with your Google ID to app inventor and start developing on it. First, you develop the UI in app inventor and then add functionality in your app.
4) IntelliJ IDEA: This IDE from JetBrains now supports Android in its Community Edition.
5) MonoDroid For Visual Studio - MonoDroid is a plugin for Microsoft Visual Studio which allows Android application development using C# and .Net technologies. Installation is straight forward and easy.