As gllampert pointed out in the comments the value is hardware dependent. You can retrieve it with [glGet][1], using `GL_MAX_COMBINED_TEXTURE_IMAGE_UNIT`. You can find how different hardware performs [here][2].

However, in OpenGL 3 there is a lower bound of **at least 48 simultaneously used textures**, no matter which type. [[source][3]]


 [1]: https://www.opengl.org/sdk/docs/man3/xhtml/glGet.xml
 [2]: http://delphigl.de/glcapsviewer/gl_stats_caps_single.php?listreportsbycap=GL_MAX_COMBINED_TEXTURE_IMAGE_UNIT
 [3]: https://www.opengl.org/sdk/docs/man3/xhtml/glActiveTexture.xml