From Satellite TV FAQs

There are Satellite TV guides available that have a partial listing of
what is in the sky, and these also include program listings for the
various regular program services. You should be able to find at least
ONE of them at any news stand. ORBIT and ONSAT are the two most widely
available guides. ORBIT is a huge monthly book, and ONSAT is a weekly.
Satellite TV week also is a weekly in a tabloid format.

If you are just interested in knowing WHAT is up there, and desire a
comprehensive listing of ALL the satellites and Channels, there is no
finer list than the SOUTHSCANNER CHART, which is available here in
Homesat/rec.video.satellite every month. If you can't wait, write for
your copy (It is huge, about 100 pages long if you PRINT it) and has
full information about every occupied transponder in the [Geosynchronous satellite] arc.

The LyngSat Guide lets you select individual satellites to see what their transponders are offering.

DirecTV offers 225 channels

The Satellite Control Center provides extensive information on the number of channels broadcast by all GEO satellites and lists literally tens of thousands of channels including TV, radio and data.

The King of Sat resource has a satellite channel directory and if you add up the numbers for TV programs listed from A to Z you get 3102 :

[0-9] = 28

A = 226

B = 150

C = 269

D = 111

E = 125

F = 88

G = 56

H = 74

I = 88

J = 38

K = 95

L = 65

M = 205

N = 130

O = 67

P = 194

Q = 12

R = 141

S = 366

T = 401

U = 45

V = 77

W = 34

X = 14

Y = 12

Z = 20

Total = 3102 TV programs