Something like this:

    open FH, "foo" or die "Can't open foo: $!";
    while (<FH>) {
        ## current line is in $_, process it
    }
    close FH or warn "Error closing foo: $!";
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If these are files specified on the command line, you can use the special construct:

    while (<>) {
        ## line is in $_
    }
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    $ process.pl foo.txt bar.txt baz.txt
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Don't forget about the everfaithful -i.bak command line flag. It's one of my favourites. It edits a file "inplace" one line at a time. This should delete everything that doesn't contain the string "foo" (but I haven't tested it. sorry)

perl -epi.bak "print if(m/foo/);" foo.txt bar.txt baz.txt
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Update:
Read on for the correct answer. I really should have tested it. Thanks Mirod and Btrott. ++ to both of you. -- for me.

You really should have tested it:

• -e should be immediatelly followed by the script to run,
• -p prints the current line, so you don't have to do it yourself, -n is what you want in this case.

This (tested!) script would work as:

perl -i.bak -n -e"print if(m/foo/);" foo.txt bar.txt baz.txt

From perldoc perlrun:

-n   causes Perl to assume the following loop around your
            program, which makes it iterate over filename
            arguments somewhat like sed -n or awk:

              LINE:
                while (<>) {
                    ...             # your program goes here
                }
            "BEGIN" and "END" blocks may be used to capture
            control before or after the implicit program loop,
            just as in awk.
 
       -p   causes Perl to assume the following loop around your
            program, which makes it iterate over filename
            arguments somewhat like sed:

              LINE:
                while (<>) {
                    ...             # your program goes here
                } continue {
                    print or die "-p destination: $!\n";
                }

            If a file named by an argument cannot be opened for
            some reason, Perl warns you about it, and moves on to
            the next file.  Note that the lines are printed
            automatically.  An error occurring during printing is
            treated as fatal.  To suppress printing use the -n
            switch.  A -p overrides a -n switch.
 
            "BEGIN" and "END" blocks may be used to capture
            control before or after the implicit loop, just as in
            awk.
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Right, -i is quite cool. But all -i does is open the file for in-place editing; it doesn't "edit the file one line at a time". If you notice, you also have the -p option in the above command line; that's actually the switch that's doing the line-by-line processing.