How can I let users create their own playlists of a particular content type?
Flag module

Use the Flag module to create 1 flag for each of the lists you want to use it for (do NOT make it a 'global' flag though). The flags are to be created by an admin, but each user (authorized to use a flag) will then be able to build their own "lists" using such flag.

Then create a view (with the views module) for each such playlist you want, whereas you create a "views relationship" with one of those flags.

This approach requires the types of flags to be pre-defined (via admin), such as playlist-flags named like Bookmarked, Revisit Later, Add to my queue, Played, etc. Though it is ony like a 5 min admin update to add any other relevant flag later on (eg if a user requests another variation).

If you're not familiar with the Flag module, checkout the set of 8 video tutorials about the flag module.

You might also want to look at some of the Flag related modules, such as (partial list):


Views, to create lists of flagged content, users, etc, such as in the video about Creating global flags and listing flagged content in Views.
Rules, to trigger rules for anything that is flagged, such as in the video about Triggering rules with Flag, or to set flags with the Rules module, such as in the video about Setting flags with Rules.
Flag Lists, to allow users to create custom lists.
Flag Weights, to add weights to Flags (to be used for sorting).
DraggableViews, to make Views draggable (so that they can be rearranged by Drag'n'Drop.).
Flag Friend, a pre-built flag for marking other users as friends (using the Flag module).
Flag Abuse, a pre-built flag for marking offensive content, with some extra administrative features.
Flag, Hide &amp; Mute, for users to hide individual nodes, such as site-wide announcements or advertisements, and/or to suppress all posts by users they do not want to see.
Flag Files, to flag media files.
Flag Service, to allow Flag to be accessed via a web services interface through the Services module.
DLike, provides a Facebook like "Like" functionality using the Flag and Lightbox2 module.
Conditional Flags, provides an extra API to Flag module, for custom conditions between flags.
Organic Groups Flag Integration, extends the flag module with organic groups support allowing the administrators of each group to override the global flag settings for their group.
Context Flag, allows the use of Flags as conditional triggers for use with the Context module.


Refer to its community documentation for way more details.

Entity Reference module

Create a content type like "Playlist" for which each user should be able to create/edit "their" nodes for (with 1 node for each Playlist they want). And add a field in it using the Entity reference module for it (with multiple values allowed). Combine this with the Node Access module to ensure that each user can only "edit" their own Playlist nodes.

Other usecases

Refer to my answer to How to motivate visitors to comment (technically)? for other usages of the Flag module as illustrations of other great things you can do with the Flag module, and some other great modules that play well with it (i.e. the Rules module).