Providing links to (or, in some cases, like videos, embedding) material that's on the open web or already available to your users (from a library, etc) rather than copying it is one way to avoid the whole question. 

However:

1. Linking to/embedding stuff that's obviously infringing could get you in trouble for contributory infringement.
2. Some material may be available to you under restrictive licenses that forbid linking or embedding.