NO file in ~ has to be owned by root.
If a software requires that a file in your home directory be owned by another user, it is a bug and should be reported as such.
Other than that, a common case involves two security-related software that require restricted permissions on certain files, namely:
- SSH
- GPG
SSH
See man ssh, section FILES:
~/.ssh/config
This is the per-user configuration file. The file format and
configuration options are described in ssh_config(5). Because of
the potential for abuse, this file must have strict permissions:
read/write for the user, and not writable by others. It may be
group-writable provided that the group in question contains only
the user.
~/.ssh/identity
~/.ssh/id_dsa
~/.ssh/id_ecdsa
~/.ssh/id_ed25519
~/.ssh/id_rsa
Contains the private key for authentication. These files contain
sensitive data and should be readable by the user but not accesâ
sible by others (read/write/execute). ssh will simply ignore a
private key file if it is accessible by others. It is possible
to specify a passphrase when generating the key which will be
used to encrypt the sensitive part of this file using 3DES.
Other files like authorized_keys, known_hosts, etc. should be writable only by the user, but can be world-readable.
GnuPG
~/.gnupg (and contents) should be accessible only by you. With other permissions, GPG will complain about unsafe permissions.