ASC is data format. An ASC file contains information about the size and geographic location of the data in the file.
the ASC header must contain Geographic coordinates, with datum WGS84
So where can I get some ASC data?
There is no magical single source for such data, as this is a format. So using something like Global Mapper or ArcGIS,etc, you can convert any height data you have, into ASC , for use in DEM Earth.
So it is not just a matter of "going somewhere" and downloading some ASC data. You need a data source, which you then save out as ASC.
Global mapper and Esri offer some higher res data sources, but there is no world wide coverage from a single provider yet( see Astrium WorldDEM..)
There are commercial providers such as Intermap who can sell you better than 30m data, and they will charge you a lot for that data, and to reproject it for you.
Some countries now offer higher resolution data for free, but the amount of data involved is huge and you have to process it to ASC yourself.
In general, each country has its own data agents and you will have to find local experts to supply, if you need accurate high res data. It is an industry and in general , they are not giving anything away that is of any value. So dont expect it to be like google earth, where you just see the entire planet. Thats not how the GIS industry works in reality.