Save contacts - Save contacts app provides features through which users can select the desired data to create the backup in a variety of different formats.

SMS Backup+ - Backup Android SMS, MMS and call log to Gmail / Gcal / IMAP - jberkel/sms-backup-plus

SIM Contacts Manager - SIM Contacts Manager app offers features that let you insert your sim card to your mobile phone to manage, edit, add, and delete your contacts right at your fingertips.

SMS Backup & Restore - Simple Android app that backs up and restores your phone's text messages, and call logs too

My Contacts by Captain Tushar - My Contacts is an app by Captain Tushar that comes up with features to help you in managing your contacts list so you can effortlessly delete or edit existing contacts.

Epistolaire - Open source SMS and MMS backup app. Can convert to HTML, XML, Maildir (for emails).