We still deliver in a range of formats - USB flash drive with care instructions, DVD copies x2 (backup and also an option to give to the parents and an online gallery. We also include a set of prints because to us its always nice to hold or see your images right away, specially when we meet them to deliver the photos.
Images are in two sets, one hi-res and another set in lower-res for easy sharing.
This was from a few years ago now (our old usb flash drive design and DVD cases)
Sometimes when it is too costly to send the entire box, we will just send the flash drive or upload the hi-res onto dropbox for them to download.