I develop an open-source GIS called Whitebox Geospatial Analysis Tools that can be used to perform a range of tasks geared towards processing LiDAR data. It works with the popular LAS file format as well as shapefiles. The software can be used to interpolate raster grids, including bare-Earth DEMs and vegetation canopy models. Many of the interpolators are specifically developed to handle LiDAR data. It can also be used to examine LAS metadata, convert LAS files into ASCII or shapefile formats, tile LiDAR data, and assess point density. There are many tools available in Whitebox for analyzing LiDAR interpolated DEM files as well. This includes everything from typical digital terrain analysis operations (slope, aspect, measures of relative landscape position, etc.), hydrological analysis (e.g. extract watersheds and map streams), removal of off-terrain objects, filling in missing data holes, etc. For more information, I have a blog that describes the use of Whitebox for processing LiDAR data here. I teach GIS and remote sensing courses and have used Whitebox in LiDAR labs before. Here is an example (though dated now) lab assignment that you may find useful as well. I'm fairly responsive to requests, so if there are some LiDAR related analysis functions that aren't currently in there, send me a request and I'll add it to my To-Do list. One current limitation is that Whitebox doesn't contain a 3D point cloud viewer. I'm working on this, but if point cloud visualization is your main interest, then at the moment, you'd be better looking at something like plas.io.
LAS files can now be natively displayed within Whitebox's map area: