Ok, maybe this topic will be interesting to some. I am not an expert regarding DEMs so if you have other suggestions or you want something to be changed or added in this topic feel free to express your opinion here. Here you can find links to some free sources of DEM data for the World I have found:
ASTER GDEM - (The best one!) The Ministry of Economy, Trade and Industry of Japan (METI) and the National Aeronautics and Space Administration (NASA) collaborated on a project to develop ASTER GlobalDigital Elevation Model (ASTER GDEM), a DEM data which is acquired by a satellite-borne sensor "ASTER" to cover all the land on earth. Latest Version of ASTER can be obtained after filling [Only registered and activated users can see links. ]. (Very boring thing. Need a couple of weeks waiting. Faster you can download the desired ASTER DEM via [Only registered and activated users can see links. ]. (see this [Only registered and activated users can see links. ] for more info) )
ACE2 - The ACE2 Global Digital Elevation Model is available at 3", 30" and 5' spatial resolutions:
[Only registered and activated users can see links. ] - The Shuttle Radar Topography Mission (SRTM) is obtained elevation data on a near-global scale to generate the most complete high-resolution digital topographic database of Earth. SRTM consists of a specially modified radar system that flew onboard the Space Shuttle Endeavour during an 11-day mission in February of 2000. SRTM is prior to the realese of ASTER GDEM.
SRTM is an international project spearheaded by the National Geospatial-Intelligence Agency (NGA) and the National Aeronautics and Space Administration (NASA).
SRTM 30 Plus DEM - SRTM30plus data consists of 33 files of global topography in the same format as the SRTM30 products distributed by the USGS EROS data center. The grid resolution is 30 seconds which is roughly one kilometer.
Land data are based on the 1-km averages of topography derived from the USGS SRTM30 grided DEM data product created with data from the NASA Shuttle Radar Topography Mission. GTOPO30 data are used for high latitudes where SRTM data are not available.