What does the rest of the panic say? You might need to use the 'logview' command from the Linode LISH shell to do it (not your system's console):
ssh
linodexxxxx@citynameyyy.linode.com logview
Password: (your LISH password, set on the Remote Access page)
I'd bet a substantial portion of the cash in my wallet it will say "Free swap = 0kB" in there. If so, you're running out of memory. I'd also bet on Apache and PHP being involved... if you're using PHP-related stuff and Apache, check your apache2.conf's MaxClients setting in the mpm_prefork section. If it's greater than about 25 or so, you're likely to have a bad time.
(The default is 150, for reasons we'll chalk up to naive optimism guarded by a fierce bureaucracy.)