Depends highly on the update, you always stand the chance that a new update will be itself a security risk, or expose one while addressing another, but you also can assume it will be widespread,, and that by adopting it early you enter a large pool of recent known attack targets.
I agree with sschroeder, it depends on the environment, for the average home user, I would say yes, because most are safer at least trying. In corporate environments I say no because if not insecurity brought with new patches, may come instability, and deploy nothing large scale until well tested. Exceptions being those cases where you just have to because the internet is on fire and your dongle is exposed.
This is especially true of service packs, where an individual update is generally highly tested and highly specific, service packs could make thousands of changes to a billion different system configuration possibilities, I have seen entire companies brought down my automated install everything automatically strategies of admin who favored ease of false security over diligence, competence, and stability.
As far as security goes... A good approach to all secure environments is system hardening... so if an exploit is found, what can a remote user do with it? Proper firewall rules, allowed traffic, protocol analysis, at the borders. Disabling unneeded protocols, services, and utilities on the machines themselves. I mean ultimately in the hands of a gifted attacker, there is almost always a way, however those types are in general rare, more often it is the passerby looking for vulnerable systems, and you can do a LOT to make yourself a less worthwhile target.
Those things give you the ability to carefully plan update strategies instead of install and pray.