If I am not mistaken, programs like Spotify or Steam are not included in any of the Ubuntu repositories (main, restricted, ...). And I guess they will never be?
Correct me if I am wrong.
If I am right, is there a ppa that provides a collection of closed-source, non-free software and takes care of updates?
First of all, a PPA is just one form of a software repository. PPAs are special ones, as they're hosted on Launchpad and must comply with the rules there. A general software repository (privately hosted) can hold whatever packages someone put in there.
Is there a ppa that provides a collection of closed-source, non-free software?
No, PPAs will accept source-only uploads as a policy, by design. The binaries will be built "in the cloud" of Launchpad and both binaries and sources are published in the PPA. So, unless Spotify or Steam are releasing all relevant code (and comply with all packaging+licensing requirements), it will not be possible to publish this in a PPA.
Please refer to "How do I submit a binary?" on Launchpad and this very similar question: "Can I upload binary packages to a Launchpad PPA?".
As mentioned by @dobey, one could make a source package consisting of binary blobs (precompiled binaries), with no need to compile at Launchpad anymore. However, this is rather a hack and outside the terms of use for Launchpad PPAs. source in "source package" does not mean anything in such a case. Having several of these packages to just to "collect" several pieces of software for the convenience will not exist very long.
Software vendors can (and already do) publish this in a private (binary-only) repositories (e.g.Google Linux repositories), or, Canonical may include them in the extras and/or partner repositories. This is how Skype and Adobe Flash Player are being distributed by an "official" Canonical-maintained repository, easily accessible for all Ubuntu users. Also, the MyApps project as proposed by @dobey is an example for a way closed-source software can be maintained in a repository. However, for MyApps, this has to be on the initiative of the vendors.
