It might bear mentioning that you can also get saves from being in cover - cover saves.
3+ armor saves are pretty great, but there are so many things that can punch right through them. This is especially true because there are so many units with 3+ saves - it's always a good idea to stock up on weapons with AP>3. I run as many as possible in my Space Wolves list. Which means that anything with a save of 3+ ( or worse, god help them ) would not get to take a whole lot of saves. Invulnerable saves remedy this problem, but so do cover saves.
If you're in cover, you might lose your armor save - but you'll still get your cover save ( assuming no weapons used ignore cover ). A cover save may be worse than your armor save ( depends ), but it's a whole lot better than nothing.
So, to summarize: More saves gives you additional 'layers' of protection, whenever one layer gets stripped away. And don't trust armor saves. It's not that they aren't useful, but you should never just assume you're going to get to use them.
EDIT: I'd also like to take this opportunity to just ... once again point out that Space Wolves' Helfrost weapons are B-A-N-A-N-A-S. It's not that they kills you instantly if you suffer an unsaved wound ( which you will given the weapons' profiles and the BS of the units they're mounted on ) - it's that they don't. Because if they did, units with the Eternal Warrior rule might still survive. Helfrost circumvents that entirely. Good god, they're terrifying.
Okay. Okay, I'm done now.