Single player games on Steam that require you to log on to other services?

EA games on Steam apparently require you to log on to Origin,

They do? If I'm not mistaken, there are no games on Steam that requires origin.

A lot of games by Kalypso Media Digital requires you to log into their servers.

I think that new Steam agreement rule about stop supporting 3rd party platforms only applies to new games, old game's won't be affected.

Gremlins Inc. req online connection to play single player, but they plan to change that on 1Q 2017

It's horrible. I tend to be much less interested in acquiring a game legally if it pulls this sort of crap.

If I recall correctly (and it hasn't been patched afterwards, I think not), there was a game called The First Templar released on Steam something around five years ago or so which required you to log in into four separate accounts in order to play online with your friend. You needed Steam account, Kalypso account (publisher), First Templar account (for whatever reason, great idea) and Facebook account for online play. It did not sell well.

EA account (not Origin) for the few remaining EA games, Uplay for Ubisoft, Kalypso Launcher, Rockstar Games Social Club, Denuvo (not DRM, but relies on a third-party server)... and the infamous Games For Windows Live.
There're quite a few third-party services on Steam games. A good, albeit possibly not complete, list is on PC Gaming Wiki

It does not apply to all the games, it is on a game by game basis.

For example, I played Grow Home which is a Ubisoft game and I was able to install and play directly through Steam, but Far Cry 3: Blood Dragon required me to install Uplay and create an account. It basically just launches from Steam, but required you to log into and have Uplay running as well.

If you look at the store page for Grow home it says "Requires agreement to a 3rd-party EULA Grow Home EULA", while Far Cry says that and also "Requires 3rd-Party Account: Uplay (Supports Linking to Steam Account)".

The only game that I'm happy to log on to a third party service for is Pulsar: Lost Colony, and that's only because it's in Early Access, and local co-op, single player, and their own servers are further down the roadmap. "Log on" may be the wrong word for it as well, as no account is required.

Fully released/AAA games? Not a chance.