This number is somewhere between Googol (10^100) and Googolplex (10^(10^100)). Or more precisely between 10^(10^22) and 10^(10^23).

The number of all colors modern graphic cards can represent is: 256^3 = 16.7M
The number of pixels in a full HD image is 1920 × 1080 = 2M

Now to get to the number all full HD we have to put (256^3) to the power of 1920 × 1080.

(256^3)^(1,920*1,080) = 1.5... × 10^14,981,179 = 10^(10^7.17...)

Let's call this number HD.

As a comparison Googol, a very very large number, is equal to 10^100. So HD is much greater than Googol but smaller than Googolplex (10^(10^100)).

Now onto movies. Let's assume they are silent movies, with no audio. Let's assume they last 90 minutes and are are filmed in 48fps.

So we get 90 * 60 * 48 = 259,200 frames.

Since every one of the 259,200 frames can be any of the HD images the number of all HD movies is

(10^(10^7.17...))^(0.26 * 10^5) ~= 10^(3.83 * 10^12)

Now for every conceivable soundtrack. Sampled at 44.1kHz and with 16bit resolution per each of the stereo channel has 90 × 60 × 44100 samples so there's (2^32)^(90 * 60 * 44100) different soundtracks i.e. around:

~10^(10^9.36).

In total you can have roughly 10^(10^22) different movies.