I agree that it's annoying to get emails at 2AM. I have an android set up with my work account (Exchange) as well as my Gmail, so I have set them to use different tones, the Gmail tone is a light beep that is easily missed, while the work email makes a sound that's much harder to ignore.
I've set up a ton of filters trying to ensure that only important emails show up as New, and anything else bypasses my inbox or gets marked as read immediately so I don't have to hear it on my cell phone. This works somewhat, but I'll still get new messages that haven't been filtered yet occasionally.
If you're on an Android, there are some apps that will silence your phone at specific times. LOCALE will let you change ringtones based on GPS location or on time of day, so you can silence your notification whenever you're at home, or from 10pm to 6am or something. There's also one called SHUSH that will set a timer whenever you silence your phone, so you can turn off your ringer when you go to bed and then it can turn itself back on after X hours. (These won't alert you for real emails, but will at least let you get a good night's sleep.)
If you use GMail primarily, you can also set up multiple addresses using a + sign after your ID. For example, I always sign up for newsletters with firstname.lastname@example.org and filter those to skip my inbox automatically, so they don't make noise on my phone. You could also do one for email@example.com so your important emails come through loud and clear, and then just tell everything else to skip your inbox or to be marked as read automatically or something. This saves a lot of time because you can filter everything TO that address, instead of having to set up a new filter each time you sign up for a newsletter or create a new notification alert.
That + in addresses is a very handy feature, but it's not very well-known or advertised.