MySQL CPU & Memory Spikes
I remember to have the same problems and it has something to do with how vBulletin is programmed. Please check regular "cronjobs" (not talking about system cronjobs you have already mentioned not to be the culprit) run by vBulletin which are triggered by visting users.

You can find them in version 4 of vBulletin in your admin panel, just below the settings for RSS-Feeds.

Another point to check is wether your vBulletin tables are in MyISAM format. vBulletin (at least until version 4) is optimized for MyISAM - if you happen to use InnoDB then some queries on vBulletin's tables (especially with the post table) will literally grind your system down to a halt.

Hope this helps.