We know that RDF is the cornerstone for semantic web. So we can use RDF for describing electronic libraries, content for search engines, time schedules for web events etc.
However, can we apply the RDF model to 'non-semantic' web applications? Are there any examples?
You can use RDF in the frontend and/or in the backend.
As soon as you use it in the frontend (RDFa in HTML, separate RDF files, etc.), you play a "part" in the Semantic Web. There are no websites/applications that couldn't make use of RDF.
If you use it in the backend only (database, import of RDF data, etc.), you don't publish any RDF, and therefor there is nothing "semantic" about your site/application itself. It might consume Semantic Web data, but it doesn't produce it.