Recently I downloaded the Gmail app for my iPhone, in spite of some bad reviews on it. So far, I've found it to be a really nice alternative to the native email application on my phone.
I can view my both of my Gmail accounts and I can choose to get notifications for only the ones that I want to see. I use one as a spam catch all, so I definitely don't want to see notices pop up all day long for a bunch of emails on sales at my favorite store, or whatever.
It works much better with deleting - when I use the built in email tool on my iPhone, it doesn't really "delete" things from my Gmail, so then I have to delete them all again the next time I'm online. I've always found that to be annoying, since I like to keep my inbox pretty empty.
I can easily flag emails as "important" or "starred" using the Gmail tool on my phone. I use the "important" flag for personal items and I use the "starred" flag for business items. It helps me to filter my view when I want to find something, even if I've labeled it and moved it out of my inbox.
Overall, I'd recommend the Gmail app to anyone with an iPhone. I find it much better to use for Gmail than the native iPhone email app.
If you have the Gmail app on an Android or Windows phone and would like to share your experiences, for the good or bad, please feel free to comment.