Most of the answers have become a bit dated so here is an update: Nandroid Manager doesn't seem to be developed any more and doesn't work reliably with the latest versions of Android anymore. But it's worth a try. In my case, about half of my apps were successfully restored and for most of the ones where "restore app + data" failed, "restore data" alone worked (and you can just reinstall the app from the app store).

As regards Titanium Backup Pro, it is still updated but the "Restore from Nandroid" function doesn't seem to work too well either on Marshmallow. Over the past months, there have been multiple reports of it either not seeing the backup files at all or failing to read their contents. I guess it's not a priority for the developers to fix this.

Most of the answers have become a bit dated so here is an update: Nandroid Manager doesn't seem to be developed any more and doesn't work reliably with the latest versions of Android anymore. But it's worth a try. In my case, about half of my apps were successfully restored and for most of the ones where "restore app + data" failed, "restore data" alone worked (and you can just reinstall the app from the app store).

As regards Titanium Backup Pro, it is still updated but the "Restore from Nandroid" function doesn't seem to work too well either on Marshmallow. Over the past months, there have been multiple reports of it either not seeing the backup files at all or failing to read their contents. I guess it's not a priority for the developers to fix this.