Yes, and to a shocking degree. Around where we live, there is roughly one star per 19 cubic parsec. In the center of the galaxy, there are as many as 10 million stars per cubic parsec, and did some clusters there are more like 20 million.
That makes the average distance between stars at more like 500 to 800 AU, which is still 12 times the distance between the Sun and Pluto, but if you lived in that area the night sky would never get darker than twilight here on Earth.