I finally found an Otaku in an Anime!!!

[u2205]

There was a random side character in Darker than Black Ep. 17 that said he came to Japan to study Anime! YAY!!!

[pieisexactlythree]

There's one in Paprika, as well as in Paranoia Agent. 

[pieisexactlythree]

Also, I think Koushi Rikudou, who appears as himself in Excel Saga counts.

[AzuKyo]

Genshiken features a cast of Otaku. Although, I think you're refering to non-Japanese otaku.

One of the new Lucky Star characters is an otaku. Genshiken (manga) also features two foreigners who are really into anime (they're Ohno's friends from America).

For otaku (western and Japanese) in anime, I strongly suggested Otaku no Video.

[superjaz]

There was a random side character in Darker than Black Ep. 17 that said he came to Japan to study Anime! YAY!!!

um are you jokeing?
what about renge in host club?

[balmno]

there's otaku in welcome to the NHK also.

[TomtheFanboy]

Bah! There have been otaku in anime forever!

Heck, there's a whole anime that's just about a bunch of Otaku trying to make an anime!
Oh, and how about the Betamax guy in Cowboy Bebop, or the two dudes in DigiCharat?

I think that 3 internets should be awarded to the person who finds the OLDEST otaku character in an anime, and the Daikon opening movies don't count!

[AzuKyo]

I think the oldest reference to an otaku in anime is in Macross, which I believe the oldest actual otaku in anime are found in Otaku no Video. Old school anime didn't have as much as a focus on modern society like newer anime does, so it wasn't probably "in" to have an otaku character until Gainax broke the mold.

However, there's a good chance that there were anime-obsessed (while not called otaku) characters in works like Doraemon or that old manga about the Koban policeman (which is still going).