You can create both personal and team alerts in TFS from TFS Web Access. Click on picture to get full screen view.

From here we can view Work Item alerts and select one or more.

Similarly, we can add new alerts for Checkin Alerts where we can select one or more alerts.

And we can do likewise with Build Alerts and Code Review Alerts.

If you find, yourself getting too many emails for an alert, you can filter on these alerts with a rich set of filters.

Or delete the alert, choice is yours to experiment.