[mburst]

Facebook. If you really don't want others to see your photos you could make a separate Facebook account just for uploading photos. If super high res is something you care about I think Google+ offers slightly better than Facebook. Anything I want super backed up I just upload to Google Drive.

[jmathai]

If you're seriously interested in keeping your photos around for a long time (20+ years) you really ought to think about using a more resilient service and having local backups.

[deadfall]

You can mark photos only visible to yourself.

[dogan]

The apps might access to them though.