I'm pretty new to Japanese, and I've been trying to learn hiragana and katakana. I know that in hiragana, wo (を) is used only for as an object particle, and it is always pronounced like o (お).
This made me wonder what the katakana form (ヲ) would be used for, since o (オ) would be used for anything with an "o" sound. Even if a direct object is written in katakana, the o that follows would still be in hiragana, correct?
Some of the posts indicate that ヲ is very rare. This isn't really the case. In general Japanese usage, yes, it is very rare. However, if you have all-katakana text, then you will always find を written as ヲ.
All-katakana text might be encountered in child-oriented media such as video games. I have seen plenty of old games that use only katakana, such as Downtown Nekketsu Monogatari (known in the US as River City Ransom), Moero!! Junior Basket (known in the US as Hoops), and the original MSX/NES version of Metal Gear. ヲ is used in all of them. (Some of these games used all kana due to technical limitations, but sometimes all-kana text is a stylistic choice.)
In manga and video games, robots will often speak in katakana, much like using an all-caps "digital" font in English.
Transcriptions of morse code, telegrams, etc. will also use all-katakana text and therefore ヲ. So usage of ヲ is alive and well, it's just that the contexts where it's appropriate are infrequent except in certain media.
Another usage was in some pre-WWII documents, which swapped hiragana and katakana as they are used currently. e.g., ミンナガ協力出来ルヨウニ日本語ヲ勉強シマショウ。 I did a search on this and it may have been only for government documents.
~勉強シマセウ
It's sometimes used when whole sentences are written in katakana. One instance is, as Brendan noted, during WWII and for a short while after.
Another is often in comics, to indicate that the speaker is either a foreigner with a thick accent, or a robot/text-to-speech program with awkward pronunciation.
Sometimes hiragana is replaced with katakana in dialogue for stylistic reasons, or to indicate a particular speech style. For example, I have seen katakana used in place of hiragana in manga to indicate that the speaker is actually speaking another language. In those circumstances, ヲ is used as the object marker instead of を.
It is very rare and you will most likely never encounter it. I even listened to a Japanese radio show where native Japanese were saying it makes no sense to have this character anymore. The only time I have ever seen it used is when highlighting a sentence in manga, similar to how we use italics, where the entire sentence was written in katakana.
Katakana used to be used for telegrams and official documents so ヲ would have been more commonly seen. The Wikipedia article on Katakana gives a good background on how Katakana and Hiragana usage has changed over the years. Even 100 years ago it was quite different.
ヲ has practically fallen out of use these days. If you find it at all it's usually a stylistic choice, for example as notably used in new Evangelion movies together with ヱ: ヱヴァンゲリヲン.
For automated data processing, information sometimes needs to be in (half-width) katakana (older government systems, for example). There you may find ｦ in place of を (though these systems mostly store names, where を is rare anyway).
The use of katakana ヲ is quite rare indeed; as you surmise, the use as a particle is Hiragana in modern Japanese. In older dialects, Katakana was used for particles as well, however, and you can see ヲ in use there. In modern times, it's also occasionally used for ironic or stylistic purposes, such as in ヲタク.
Outside of katakana used for emphasis, you may see it in names, mostly as a stylistic variant of 「かおる」 (カヲル).
On my wife's great grand father doctor's certificate, there seems to a lots of ヲ and other than other katakana and no hiragana. Packed full of kanji.
