Yes, there is grep. It has an option for recursive directory traversal, e.g.:
$ grep -r specificstring path
With GNU grep you can restrict the searched files with the --include and --exclude pattern options.
-H ('Print the file name for each match') is the default with -r, -R and when you specify multiple files on the command line. -R also turns on recursive directory traversal but also follows symbolic links.
You can also pipe the results of grep to less for screen paging.