For short scripts, your example is equivalent to

perl -p -i'out*' file1 file2 file3
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In bigger programs eof() (note the missing parantheses) indicates a change of $ARGV. You can use that to get rid of handling $oldarg.

Update: Oops, corrected after ysth's comment. Thanks.
Update2: Clarification: The use of the -i (in-place edit) switch produces a result that is equivalent to the given (OP) example only. If you add further processing (-e), the new output will be found in the files given at the command line (file1, file2, ...) but not in outfile1, outfile2, etc. since they are the backups of the original files. So, using 'out*' for the backup filename is generally a bad idea (ill. semantics). I should have made this more clear in the original answer.

You've got it backwards. eof without the parentheses is what works between files. eof() is only true after the last file.
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In your example, "out*" will be the original file, while in the OP's code, "out*" will be the new file. Otherwise they are equivalent.

Update: And please note that errors are not checked in either case. Imho a big problem with the "-p" switch is that it does not check whether writing and closing is successful.

my @files = @ARGV;
for my $fn (@files) {
    local @ARGV = ($fn);
    open OUTPUT, '>', "out$fn" or die $!;
    while (<>) {
        print OUTPUT $_;
    }
}
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That won't work for empty @ARGV, which you'd have to special-case.

See the docs for eof in perlfunc. It gives a recipe on how you can use eof() to detect the end of each file.

It looks like you want something like this:

#!/usr/bin/perl
use warnings;
use strict;

while ( <> ) {
    if ( $. == 1 ) {
        open OUTPUT '>', "out$ARGV" or die "Cannot open out$ARGV: $!";
    }
    print OUTPUT;
    close ARGV if eof;
}
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There is. Don't use <>, use open/close and you won't have to check.