Note that a few functions behave differently if they are called with an empty pair of parenthesis (usually taken as an empty list).

• -t (terminal) filetest: defaults to STDOUT
• bless: requires an argument
• caller: returns less information without argument
• chdir: uses the home directory
• die: defaults to $@ (to rethrow an exception caught with eval) or a generic message: "Died"
• do: syntax error without parenthesis; with empty parenthesis, dies with "Null filename used"
• eof: with empty parenthesis defaults to ARGV, without parenthesis defaults to the last file read (but detects the ends of individual files read by ARGV)
• exec: it seems that the call just returns failure, I can't find anything in the docs
• exit: defaults to zero
• gethostbyname, getnetbyname, getprotobyname: requires an argument
• getpgrp: uses zero, meaning the current process
• getpwnam, getgrname: requires an argument
• getpwuid, getgrgid: requries an argument
• gmtime: uses current time
• local: syntax error without parenthesis; with empty parenthesis, is a no-op (localizing $_ could be useful, but this way is more consistent with localizing lists of variables)
• localtime: uses the current time
• lock: requires an argument
• mkdir: required an argument before perl 5.10.0
• my: requires an argument (even empty parenthesis don't suffice)
• our: requires an argument
• pack: requires an argument
• prototype: seems to just return undef, I've found nothing in the docs
• rand: uses 1
• readpipe: no idea, but it can produce segfaults
• reset: resets only question-mark searches, no variables
• return: returns empty list in list context, undef in scalar context
• scalar: requires an argument
• sleep: sleeps forever
• sort: gives a funny error message without parenthesis; with parenthesis, sorts the empty list
• sprintf: requires an argument
• srand: uses some reasonable seed
• syscall: requires an argument
• system: seems to just return an exit code 255, I've found nothing relevant in the docs
• tied: requires an argument
• umask: returns the current umask without changing it
• undef: returns undef without undefining anything
• untie: requires an argument
• waitpid: requires two arguments
• warn: uses $@ suffixed with "\t...caught", or a sensible message "Warning: something's wrong" if $@ is unset.
• write: uses the currently selected filehandle

The following functions accept a filehandle, directory handle, label, or bareword as an argument, and thus don't default to $_. (I do not list those functions that need an array or hash argument, like pop.)

• binmode: requires an argument
• close: defaults to the selected filehandle
• closedir: requires an argument
• dump: defaults to the top of the program
• fileno: requires an argument
• getc: uses STDIN
• getpeername, getsockname: requires an argument
• goto: requires an argument
• last, next: uses the innermost loop
• no: requires an argument
• open: requires an argument
• package: without argument, declares that there is no current package, but this usage is strongly depreciated
• readdir: requires an argument
• readline: no idea, I could even get a segfault (the diamond shortcut, however, defaults to the special ARGV filehandle)
• redo: uses the innermost loop
• rewinddir: requires an argument
• select: returns the current selected filehandle without changing it
• tell: uses the filehandle last read
• telldir: requires an argument
• use: requires an argument

I've compiled these lists using both the perldoc perlfunc and testing how the functions actually behave with perl (5.8.8 i686-linux). For this reason, there can be errors and omissions in this list. If you know about any omission, please contact me.

Update: added readmore.

Update 2012-12-27: added the new evalbytes function.

Update 2014-01-29: added changes to mkdir and unpack.