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Why do some people spell her name without a 'u'. Which one is proper???

Is Romanji Japanese???

They're both "correct" in the sense that there are multiple ways of changing Japanese script into English letters; romanji --also romaji--is just the general Japanese word for it (Roman, that is Latin, plus ji, letters). If you're spelling it with "Roman" letters, it's romaji no matter how it's written. As opposed to Japanese writing, which is based on Chinese characters (kanji) and two kanji-derived syllabaries, hiragana and katakana.

Part of the trouble is that English speakers don't have elongated vowels and our writing system follows entirely different rules from Japanese. So, as Relowinya said, it's ki + kyo + u ... but not everyone reads Kikyou as kee-kyohh; you can mistake it for 'kick you' or other weird combinations. If we don't have elongated vowels in English, to some people it makes little sense to transliterate them into the Latin alphabet.

...

well both are i guess but ofcaurse the orignal is Kikyou so use whatever you please.

you can write them either way, it's not like anyone would get confused if you add or take away the "U"

I prefer Kikyou.

I do too. Kikyo is weird to type...o.O