tbh, the only backup app would be from your device manufacturer.
Samsung has their app which will sync stuff to/from your PC.
Apple is "technically" iTunes, but, I don't know how much of that is your PC vs Cloud.
Everything is trying to push us to the Cloud ecosystems (yes, I understand you don't want the cloud is probably the reason you're looking to back up to your local PC). It makes it "easier" to restore to another device in the same ecosystem. The backup with a Samsung app will not restore to an LG device.
You should be able to mount your device to copy your photos and files off.
iPhone? Android? S40? Windows?
Even with root and jail-breaking, there is no 100% guaranteed back up solution for moving from one device to another. It is easier when you stick to the same manufacturer but you still won't get a 100% back up.
What all do you want to back up? Pictures are easy enough. Simply copy them to your PC or Mac. There are a bunch of apps out there that do back up texts but most don't fully support MMS or RCS. Ringtones, notification sounds, icon packs, themes and wallpapers become more of a hassle when you mix in purchased items thanks to DRM and varying device compatibility. Some settings can be backed up with the launcher but there are still some settings that aren't actually backed up by most things. Compatibility is usually the issue there.
The best way to back things up, at least in my opinion, is doing it manually. Take some screen shots of your settings, back up your images and videos to your PC, create and save your own ringtones and notification sounds, and wallpapers.
If you simply want to make a direct copy of everything on the phone then plug into PC make sure you have file transfer selected from the pool down on the phone and then open up on the PC select everything in the root folder and drag it over to a new folder on your desktop.
If you're trying to copy message logs like texts or calls Google drive does that for you automatically as long as you are signed in. You can find backup settings within the phone's main settings screen usually under backup and restore.
Google travel back up all of your apps. As well as your texts and calls. The PC method will back up everything else on the phone.
If you're using an iPhone then go to iTunes and iCloud.