Having used the Apple Watch for a little while now I've found a few notification options to be really neat.
Independent Silent Mode
While the watch comes with sounds enabled by default, and the sounds aren't at all unpleasant, a silent tap on the wrist is so much more pleasant that I quickly got used to it and stopped switching sounds on and off (which is a simple matter from the settings glance). I don't always have my phone on silent; sometimes while I'm using it the audio alerts are beneficial, but while the phone needs to be able to get my attention somehow while I'm not looking at it (remember that if it's unlocked you dont get tapped on the wrist) the watch doesn't require a line of sight in silent mode.
Independent Do Not Disturb
I like my iPhone, iPad and Mac to STFU late in the evening, though I'm often awake after this time. So when my phone goes into DND the silent and discreet taps of the Watch are still really useful for unintrusively letting me know that something is happening without having to toggle off (and remember to toggle on again) DND mode on my phone or whichever device I'm using. If it's late and I want all notifications to shut up I can just take the Watch off.
Reduced Push Notifications
I keep turning push notifications for different apps off; and some apps have become more restricted. I don't want to raise my wrist, for example, just because someone favourited a tweet. I do however want to know if someone sent me a DM; so Tweetbot's notifications which were previously all on are now cut down. I don't miss any of the notifications that I have excluded — there's probably a lesson in this. I use a fair few apps that employ notifications only very rarely and for quite specific and useful information, like parcel delivery tracking. So far I've left these enabled. Find My Friends, the Apple Store, and a handful of other's fall into this category.
This is the one I haven't quite figured out. The Apple Watch is not a great way to digest e-mail and can't even display anything with a complex HTML layout because the screen is too small. Therefore the e-mail functionality of the Watch really begins and ends with notifications; you probably want to know if you've recieved a valuable email so you can decide if it's urgent enough to stop and deal with it or if you simply need to remember to read it when you get back to your computer. I think I'm going to have to re-investigate the VIP e-mail settings before I get this right.