Should I keep updating OS X or not?

That's a myth, nothing more. Newer versions of an OS contains more code to run, more resources to load, etc, so naturally with time the OS starts to run slower on the machine you're on. It isn't apple intentionally trying to slow your computer down, it's just the natural order of things.

 

It depends, a classic example where that method of thinking is plain wrong was the jump from leopard to Snow Leopard, SL was faster then leopard on the same hardware. That being said SL to Lion required better hardware. There is no hard and fast rule imo.

 

You should keep updating as many security patches (to known flaws) are applied through software updates. There are also functionality updates, Safari updates are an example of this.

To believe that Apple is deliberately slowing your computer down in hopes that you will buy a new one is ridiculous.

You are more likely to purchase a new Mac as your next computer if you already own one, simply by the nature of Apple's customer loyalty statistics.
Apple doesn't need to slow your computer down. Computers wear our, hard drives are very common wear items (they usually last about 3 - 6 years). Oftentimes the lure of a new machine makes the choice between shelling out for a new computer and spending several hundred dollars (assuming you don't replace your own hard drive, migrate your own data, and reinstall your own OS) to have someone else fix it.

Essentially, you sell your own self a new Mac. Apple doesn't even have to try. This is part of the reason Apple doesn't do a huge amount of marketing compared to other mega-corporations.

 

In the early days of OS X there was an ongoing joke that with each new version it would feel faster than the last, whether this was true of the update cleaned up you OS which could make it feel faster.

The best thing is if you rely on your Mac for business/work then make sure software is compatible and always make sure your backup is up-to-date before upgrading, worse case you restore back to the earlier version if things go wrong.

 

While I wish I couldn't contradict you, I will. Have you used any Microsoft software lately? And I don't mean in the sense of whether or not you enjoy using it, but rather have you seen what they can make it do on even the slowest machines?

Windows 8 runs buttery-smooth on old hardware. Windows Phone 7 ran circles around android and could keep pace with iOS (for non-CPU/GPU bound use), on 2 year old hardware. Core 2 Duo hardware that Apple has long put to rest can run Windows 8 great, but it can't run the latest version of OS X because it's "too old".

I want to love Apple's software just as much as the next person, but the truth is it isn't all that great on older hardware, and it's not because it of hardware inadequacies.

 

My last Mac was a 2006 Core2Duo iMac -- the 2nd generation of Intel Macs. It came with Tiger, and I upgraded to Leopard, Snow Leopard and Lion.

Snow Leopard brought the most noticeable quickening, but Lion was certainly no slower than that. I would say each OS was at least as fast as its predecessor. It wouldn't run Mountain Lion -- but perhaps the reason for that delineation is that ML would have been super-slow on it. Perhaps.

I've been using OS X since 10.2, and in my experience Leopard was the only OS where older hardware noticeably struggled.

My general advice is to stay current (i.e. up-to-date).

 

Keep updating. A new system update isn't going to have a critical impact on your machine. I too worked with a Late 2006 Core 2 Duo MacBook Pro and it did very well for me with Tiger-Lion and it only got better with every update.

And on the late 2011 model I am using right now, the Mountain Lion update made a HUGE difference, stability wise even.

Don't let updates scare you, if it wasn't okay to begin with, they wouldn't let you run it.

 

No, I mean stay up-to-date.