Websites

http://cve.mitre.org [news section] [search/cve/keyword]
https://www.debian.org/security/
https://www.ubuntu.com/usn/
http://people.canonical.com/~ubuntu-security/cve/
http://www.slackware.com/security/

Mailing lists

https://lists.ubuntu.com/mailman/listinfo/ubuntu-security-announce

Update & Verify

Redhat

yum updateinfo list # get a list of vulnerabilities

yum updateinfo RHSA-2017:0149 # get more detail about a specific vulnerability

Check integrity - verifing packages

rpm -Va # verify all installed packages

ubuntu

apt update

apt full-upgrade

apt-get dist-upgrade

apt list --upgradable |& grep security # show only a list of security updates

linux-generic/xenial-updates,xenial-security 4.4.0.71.77 amd64 [upgradable from: 4.4.0.70.76]
linux-headers-generic/xenial-updates,xenial-security 4.4.0.71.77 amd64 [upgradable from: 4.4.0.70.76]
linux-image-generic/xenial-updates,xenial-security 4.4.0.71.77 amd64 [upgradable from: 4.4.0.70.76]
linux-libc-dev/xenial-updates,xenial-security 4.4.0-71.92 amd64 [upgradable from: 4.4.0-70.91]
linux-tools-common/xenial-updates,xenial-updates,xenial-security,xenial-security 4.4.0-71.92 all [upgradable from: 4.4.0-70.91]
linux-tools-virtual/xenial-updates,xenial-security 4.4.0.71.77 amd64 [upgradable from: 4.4.0.70.76]

landscape -> https://landscape.canonical.com/

Check integrity - verifing packages

apt search --full --names-only debsums

Sorting... Done
Full Text Search... Done
debsums/xenial,xenial 2.1.2 all
  tool for verification of installed package files against MD5 checksums
  debsums can verify the integrity of installed package files against
  MD5 checksums installed by the package, or generated from a .deb
  archive.

debsums -es |&  grep --color=no "missing" # e= config,  s= silent

debsums: missing file /etc/default/chromium-browser (from chromium-browser package)
debsums: missing file /etc/init.d/keyboard-setup (from keyboard-configuration package)

debsums -a &> debsums.log