What are some examples of Non-Treasury securities?

I understand that a credit spread means the widening between the yield on Treasury vs. Non-Treasury securities. Would corporate bonds, for example be an instance of Non-Treasury Securities because they are not backed by the US Government?

Yes, credit spreads in comparison to T-Bills can be drived from any fixed income security or credit.

There are lots of non-treasury bonds in the market.

Bonds that are guaranteed by the government are not considered as treasuries even they bear the same credit rating as a result of the guarantee.They may still have a very slight spread to treasuries due to reasons other than credit condition.

Corporate bonds are certainly non-treasuries, even they can be rated as the highest available credit rating,i.e.AAA. They will still be traded at a spread to treasuries, as treasuries are considered as the safest within the country so any corporations within the country can not be rated higher than sovereign.