Im looking for some software that can regularly backup (eg. nightly) of all the virtual machines on an ESXi server? Or can I just run normal backup software from the running virtual machine?
Yes, you can run normal backup software from within the virtual machine. That's an easy approach if you have an existing backup infrastructure.
If you step to a higher-tier of VMware with a license (Essentials Plus or greater), then VMware's vSphere Data Protection software can handle backups for you.
You can do application backups, OS-level backups from the VM and VM disk-level backups from the ESXi host. Some places do all of those. Don't think about what needs to be backed up, think about what needs to be recovered. Does it make sense to restore an entire VM when you only need one database or one set of files?
I'm surprised nobody mentioned this, but your can always use the ghettoVCB script to, written by Iamw, a VMware employee/engineer/vExpert. It's far from enterprise-grade, but if you're running a small shop, want VM-level backups, and don't have a subscription, it works really well. Check it out here: https://communities.vmware.com/docs/DOC-8760