Many publishers allow you to sign up for email or RSS alerts when books and/or journals are published. With these alerts, you will receive information faster than a database alert, but the alerts will be narrower in scope and cover less new titles. Some alerts will also include items still "in press" that are not yet published. Some publishers have Twitter feeds you can subscribe to.
Do I have to have a subscription to their journal(s)?
If you are interested in being alerted when an author has a new book published, you can look at the author's site for a newsletter to subscribe to or you can use this website to be alerted when a new item of theirs is added to Amazon. (This site only pulls information from Amazon.) Some publishers and databases also let you set up author alerts too, but, again, the scope is narrower.
I've subscribed to alerts but can't get to the articles. They want me to pay.
Here is a list of academic publishers where you can sign up for alerts. These are for journals and articles unless noted as a book alert. (For a list of database alerts, go here.)
This is NOT a complete list. If you don't see the publisher you want, you can type the name of the publisher you are interested in into this custom search box, and their RSS or email alert service should open in another window or tab and appear in the list of results.