QGIS Table Manager plugin does not appear

In QGIS 2.8, you can find it either in the Vector menu, or in the left panel:

In QGIS 2.12.3 (Lyon), you will find the Table Manager plugin here.

Note that you will need to click on this icon before the menu appears.

Little tip: usually the category mentions which toolbar the plugin will be in. So for Table Manager, it is said to be in the Vector category/toolbar (which can be seen clearly in the previous answers):

Note that this is not always the case (but would be useful if it was methinks).