On my system when I check Keychain Access I often find new certificates. They get put there behind the scenes. Is that normal? When does this happen? Is there a way I can get alerted when a certificate gets added to the keychain?
Apple may occasionally approve additions to new Root CAs e.g. Verisign, who can then sign certificates for individual sites you visit.
The root certificates for OS X El Capitan are here https://support.apple.com/en-us/HT205204
I assume these are done in software updates via the App Store, but I don't know for sure.
Also your company may add additional self signed certificates for internal reasons or installing development software.
But AFAIK keychain won't bloat over time as you visit new sites, so the list should be fairly static.
If you get signed and or encrypted email from folks who use SMIME, Mail.app will helpfully add their public x509 certificates to your login keychain.
A pretty good explanation of the process can be found at Secure emails with Apple Mail