Cassette and VCR tapes should never be placed in your curbside recycling.
The film tape is a "tangler" that jams the sorting machines at the material recovery facility (MRF) and the hard outer shell is not recoverable or recyclable in a curbside collection.
There are some specialized plastics recyclers that may be willing to accept the hard plastic outer shell as a special drop-off item and recycle it for a small fee. You would be required to remove the film and dispose of it in the trash. Residents and businesses can find a list of options for post-industrial and post-consumer plastic in our Business Recycling Directory. Also, Greendisk offers a mail-back option for recycling.
If you choose not to use a specialized recycler for your tapes, place them in the regular trash for disposal.