Telugu classical songs are mostly devotional or bhakti songs in praise of the gods. The rare old traditional Carnatic based classical telugu songs mp3 and the Telugu devotional songs both rare old traditional ones and new latest ones are widely available online on many sites for free download. The lyrics, videos and clips of these songs are also freely available. 

Indian classical music is principally based on melody and rhythm. The system of Indian music known as "Raga Sangeet" which can be traced back nearly two thousand years to its origin which lies in the Vedic hymns of the Hindu temples, the fundamental source of all Indian music. Carnatic music is the popular classical form of south India. Saint Thyagaraja who is considered as one of the forerunners of carnatic music wrote many of his compositions in Telugu which was his mother language and thus most of carnatic music is Telugu music based. During the olden days the devotional bhakti songs were usually sung in the temples or in the courts of the kings with the help of certain instruments like the veena, the mridangam, the ghatam, the flute, etc which provided with a base for the singer to maintain his shruti and laya.

Most of the classical Telugu songs are devotional songs in praise of the gods. Most of them are written for Lord Ganesha, Lord Krishna, Lord Rama, Yashoda, Lord Tirupati, Lord Hanuman and many other gods and deities.
The famous singers of devotional songs today are Shobha, Monica, Chitra, Uday, Sandeep, Shankar Mahadevan etc.

A list of my favorite classical / devotional Telugu songs is:
1.  Swamy Chinna Aasha by Shobha
2. Nanda Gopala by Monica
3. Aanganaleere by Chitra
4. Adi Choodare by Chitra and Sandeep.