How to subscribe to information about new vulnerabilities in selected products?

Go to CVE Details' Product or Vendor pages. There is "Vulnerability Feeds & Widgets" link there.

It allows you to subscribe to CVEs about selected vendor/product.

It is possible to make a custom list of products / vendors / keywords using Cassandra service from Purdue University. It is free and allows updates to be emailed.

secunia makes a commercial product that does exactly what you want.

"The Secunia VIM lets you create specific vulnerability management reports for different product categories across your entire IT infrastructure by filtering criteria. So you only get vulnerability alerts and intelligence relevant to your specific needs."