Best answer
In general, 秘密 (ひみつ / himitsu) is the commonly used word.
Example usage would be
秘密の扉（とびら）/himitsu no tobira (secret door) 家族（かぞく）の秘密 /kazoku no himitsu (family secret) 成功（せいこう）の秘密 /seikou no himitsu (secret(s) to success)
The word 秘密 has a bigger, generalized/longer lasting feel to it.
If you are talking about a personal secret, then 内緒 (ないしょ / naisho) , meaning “for your eyes only” or “[in] confidence/secret” is often used.
E.g.
これは内緒（ないしょ）だよ。/kore wa naisho dayo (please keep this a secret.) 内緒の話（はなし）/naisho no hanashi (secret conversation) 内緒でたばこを吸う（すう）/naisho de tabako wo suu (smoke in secret)
The word 内緒 has less formal/a little more personal/temporary feel to it.
If it’s an institutional secret, e.g. a government or military secret, then 機密（きみつ/ kimitsu) is used.
機密文書（きみつぶんしょ）/kimitsu bunsho (confidential/classified document)
So if I were asking someone to keep something a secret for time being in a friend-to-friend conversation, I’d say:
“これは内緒にしておいて。”/kore wa naisho ni shite oite (please keep this a secret for now.)
vs. If I were in an office, and talking about something I want to keep under wraps:
“これは今（いま）のところ秘密ですが、佐藤（さとう）さんは転勤（てんきん）するそうです。” Kore wa ima no tokoro himitsu desuga, Sato-san wa tenkin suru soudesu. (This is a secret for now, but Mr./Ms. Sato will be transferred to another office.)
I hope this answered your question – if more clarification is needed, please let me know.
Answer
Being the rich language that Japanese is, you get several variations. Here are a few…
化け物 bakemono or お化け obake They literally mean “something that changes its shape” or a “shapeshifter”. The reason for bringing these words up first is that bakemono is used commonly with any kind of beastly creature, and obake is often used for apparitions such as ghosts or specters, but they are really referring to living creatures such as a tanuki (raccoon) or kitsune (fox). These fall under the category of youkai. (See below)
怪物 kaibutsu This also means monster, and includes both Japanese and foreign countries’ monsters such as the Frankenstein monster or the Creature from Black Lagoon.
怪獣 kaijuu This is used mainly for huge monsters like Godzilla or Mothra.
妖怪 youkai It is a term that encompasses most monsters of Japanese folklore such as the Tengu or Kappa, which have animal features. Other youkai can have human appearance, such as the rokurokubi or nopperabou (shapeshifters), and some can conceal themselves as regular household objects.
モンスター Monstaa This is the katakana version of the Japanese pronounciation of the English word “monster”.