In my village, there's a common practice. They do Thikr (expressions of remembrance of Allaah) and send peace and blessings upon the Prophet, sallallahu 'alayhi wa sallam, in the form of songs, but without musical instrument. What is the ruling on that?

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger. 

Thikr and sending peace and blessings upon the Prophet are among the greatest acts of worship that get one closer to Allah. However, singing reported Thikr with a tune, like songs, even if it is without music, has no basis in the Sharia as far as we know. This is the practice of the ignorant people from among the Sufis, and it is closer to innovation.

The Prophet said, "Whoever introduces into this matter of ours (Islam) that which is not a part of it, it will be rejected.” [Al-Bukhaari and Muslim]

Allah knows best.