The National Information Security and Geospatial Technologies Consortium (NISGTC) a Dept of Labor funded center has posted five courses as part of the National Training and Education Resource site. Topics include intro to GIS, cartography, remote sensing and all are based on the Department of Laborís Geospatial Technology Competency Model (GTCM) -

These training courses are well written, and can be used without the labs so GIS software in not necessary to benefit from the courses, but the hands-on experience provide through the labs are a valuable addition. The labs Iv'e looked at are written for ArcGIS 10.1, but they could be adapted for other software, including the free OSGeo-Live suite of geospatial software - Once you register on the site and access one of the courses, you can take the course online or download all of the training materials, labs and data - (very cool!!!)

Geospatial Technology, Introduction to Geospatial Technology (Course) -

Geospatial Technology, Spatial Analysis (Course) -

Geospatial Technology, Data Acquisition and Management (Course) -

Geospatial Technology, Cartographic Design (Course) -

Geospatial Technology, Introduction to Remote Sensing (Course) -

NTER is an open source suite of browser-based software solutions built to help institutions develop, deploy, and manage educational and training courses for audiences of any type. This system was built with the capability to securely share content across all institutions and with the public. As an open source project, the NTER platform is free and has no licensing fees, allowing end users to free up resources for improved content development and customization. The costs associated with running your own NTER node are largely dependent on the number of users, the number of courses, and institutional IT experience to provide installation and maintenance support.