Well I want to highlight this and bring it all in this thread, as the rest of threads did not have a concluded answer, so before skipping into them here are the threads I referr
The appcompat project is a library to support android's older versions. The support library was introduced by Google recently - I don´t know in which Android version. But the point is, this project is only created when you create an Android project to cross Android platforms. I mean, when you select an old min API, e.g. API 8 (Froyo), but target recently versions, your project must have the support library. Anyway, the creation of appcompat_v7 project is some issue that has to be better configured by the eclipse plugin maintainers. However you can elegantly turn over this issue by targeting newer APIs and including in the build path the support library. This is more elegant than the others because it is better to you focus in only one android version when building your application, and when it is done, you have an authentic version of your app that you can use as a mold to support other versions, either older or newers.