We should include an alerts system into the core of 1.10. Similar to the MyAlerts plugin created by Euan.
Yes, that's a great idea!
I agree to this, it will a great feature for default MyBB

Agree with this 100%, let's bring MyBB into the future.

I agree...
However I'd like the option to use just a dropdown to display alerts rather than a modal. (MyAlerts on 1.6 looks much nicer to me than MyAlerts on 1.8)
The reasoning for MyAlerts using a Modal is that modals are built in to 1.8's JS, and the baked in dropdowns are rather poor. Were this to be in the core, it would have full core support, including the possibility of custom JS (it's easier for the team to maintain JS across versions than just me on my own).
I think this should be added as mentioned
here.
I think this one's a no brainer, it's painful using a forum without alerts these days.
I'm curious about whether it would occasionally ping the server via AJAX for new alerts, as refreshing would remove some of the benefit of having an alert system.
I support this; an alerts system is a given for forums these days.
Also, I think the alerts list should use a dropdown by default, rather than a popup/modal.