This should do the trick as well:

find . -type f -print -exec cat {} \;

Means:

find    = linux `find` command finds filenames, see `man find` for more info
.       = in current directory
-type f = only files, not directories
-print  = show found file
-exec   = additionally execute another linux command
cat     = linux `cat` command, see `man cat`, displays file contents
{}      = placeholder for the currently found filename
\;      = tell `find` command that it ends now here

You further can combine searches trough boolean operators like -and or -or, also find -ls.