If your directory structure is shallow (no subdirectories), you can simply:
find . -exec cat {} \; > newFile
If you have subdirectories, you can limit the search to a higher level, or you can consider placing some files in subdirectories so that you don't have this problem!
This is not particularly efficient, and some versions of find allow:
find . -exec cat {} \+ > newFile
for greater efficiency. (Note that a backslash before +
not required, but I find the symmetry with the previous example pretty.)
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