Yes. Sanskrit is still spoken today and the number of Sanskrit speakers is ever increasing.
In recent times Sanskrit vocabulary has been absorbed by many regional Indian languages and it can be said that the Sanskrit language lives through them.
People recite mantras and shlokas which are originally in Sanskrit.
People of Mattur village in Karnataka and Jhiri in Madhya Pradesh speak in Sanskrit due to the efforts of an organization called Samskrita Bharati. Many videos of these villages are available on YouTube.
At school and college-level, options are being provided to learn Sanskrit subjects.
Two states in India - Himachal Pradesh and Uttarakhand have declared Sanskrit as their official language.
Various online institutes/websites like Open Pathshala are coming up that teach Sanskrit online at the convenience of home.
Samskrita Bharati is an organization that has done a great job to promote/preserve Sanskrit through classes, camps throughout the world, and video lessons on YouTube.
Yes. Sanskrit is still spoken today and the number of Sanskrit speakers is ever increasing.