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I'm working in France. I thought the TanDEM-X was a free and open DEM but that does not seem to be the case.
According to a few websites, the most famous free DEMs seem to be ASTER GDEM, SRTM, X-SAR and EU-DEM.
Their spatial resolutions appear to be equivalent to between 25 m and 30 m but what other parameters such as spatial accuracy, quality of modeling, etc define their usefulness?
The answer is not as simple as the question may imply. If we had one "best one" we would not need the others, we would just use the best. Horses for courses though, needs matter.
Saying that.
This blog gives an excellent comparison of 90 m SRTM and 30m ASTER with some reasonable statistics. The winner is... well, actually you have no winner but 90m SRTM for me is nosing ahead.
The green line is SRTM and the red is ASTER.
I can say I evaluated 30m SRTM (global 30 m SRTM is now available) and 30 m ASTER for Borneo and 30 m SRTM won my race, by a furlong. You see though, I wanted watersheds and had a hydrological algorithm in GRASS specifically built for the errors in SRTM so it was not a fair race. What you want to do with it matters greatly, as does where. GTOPO30 may work great at the continental scale, whereas I need LIDAR at 1 m resolution to calculate drainage on my agricultural fields. EU DEM is at approx. 25 m and may meet your needs and all the modeling information can be found online. Actually, this is the same for GTOPO, SRTM, and ASTER as well as in the LIDAR link given. All the construction information for the major free DEMS, and many of the minor ones, exists online.
You need to decide what DEM bests fits your application and needs. We cannot do that and you have not told us your needs or even the region you are working in. You can then search online and find the information about each DEM, usually in the metadata or on an accompanying website. This list will get you started but your region may well have improved resolution sources available, such as lidar.
Here is some free literature:
Hirt, Christian, M. S. Filmer, and W. E. Featherstone. "Comparison and validation of the recent freely available ASTER-GDEM ver1, SRTM ver4. 1 and GEODATA DEM-9S ver3 digital elevation models over Australia." Australian Journal of Earth Sciences 57.3 (2010): 337-347.
Chang, Hsing-Chung, Xiaojing Li, and Linlin Ge. "Assessment of SRTM, ACE2 and ASTER-GDEM using RTK-GPS." 15 AUSTRALASIAN REMOTE SENSING & PHOTOGRAMMETRY CONFERENCE. Sydney: University of New South Wales, 2010.
Hayakawa, Yuichi S., Takashi Oguchi, and Zhou Lin. "Comparison of new and existing global digital elevation models: ASTER G‐DEM and SRTM‐3." Geophysical Research Letters 35.17 (2008).
As "@user two seven two three nine" says, it depends on what you are trying to do.
For the geosciences, there are a number of relevant papers in "Elevation Models for Geoscience", Geological Society of London Special Publication 345.
A direct comparison can be found in:
Crippen RE, Global topographical exploration and analysis with the SRTM and ASTER elevation models. pp 5-15
This also looks at combinations - eg. using ASTER imagery to improve the DEM and fill some of the voids.
Most of the other papers look at ASTER data, NEXTMap Britain, and/or LiDAR data. Some compare, some look at specific domains, and some attempt to improve - e.g. by filtering ASTER data for increase accuracy.
