With the new advent of creativity and graphics, there can literally be any design that can be produced for modern TV logos. Producers had to be more creative in the earlier days and hence, you would be surprised to know that most of the iconic TV logos that are still used widely were actual physical objects that were used for filming.
One of the most popular logo is of Leo, the Lion, who is the official mascot for Metro Goldwyn Mayer studios and you would know him roaring at the start of most of the cartoons and movies. MGM had filmed a lot of real lions to shoot the perfect opening sequence starting from 1917. However, it was only in 1957 that they shot Leo and it has been in widespread use ever since. He has been in the logo of MGM consistently for a period of 60 years and that is the longest we have ever seen.
If you wish to know more about the logo making process that was used previously, scroll down and you will see how several popular logos of the previous days were made before animation became popular. (h/t)