Nothing about Alfresco requires you to use Eclipse or any other IDE. But Eclipse is very widely used and the Alfresco SDK distribution includes Eclipse projects that can easily be imported into Eclipse, so that's what these instructions will cover.
In addition to the Alfresco JARs, dependent JARs, Javadocs, and source code, the SDK bundle has several Eclipse projects. Most of the Eclipse projects are sample projects showing how to write code for a particular area of Alfresco. Two are special, however. The SDK AlfrescoEmbedded project and the SDK AlfrescoRemote project reference all of the JARs needed for the Java API and the Web Services API respectively. The easiest way to make sure your own Eclipse project has everything it needs to compile is to import the projects bundled with the SDK into your Eclipse workspace, and then add the appropriate SDK projects to your project's build path.