There are several that I really like because of their literal meanings:
万年筆 mannenhitsu 'fountain pen', literally '10,000-year writing-brush'
兜虫 kabutomushi 'beetle', literally 'helmet bug'
七面鳥 shichimenchō 'turkey', literally 'seven-face bird' (why?)
金切り声 kanakirigoe 'shrill voice, shriek', literally 'metal-cutting voice'
Also 引っ張り蛸 hipparidako 'popular person', literally 'octopus pulled in different directions' — what a great image! It's sometimes written with the kanji 凧 instead of 蛸, thus 'kite pulled in different directions', but that's not as interesting and evidently incorrect.
I'm also attracted to words that contain reduplicating, rhyming, and alliterating elements, especially when they refer to things like chaos and confusion. So a couple of my favorite German words are Wirrwarr and Tohuwabohu, both meaning 'chaos'; the latter was actually borrowed from the Hebrew text of Genesis 1:2. Here are some Japanese examples:
ちんぷんかんぷん chinpunkanpun 'gibberish, nonsense'
めちゃくちゃ mechakucha and むちゃくちゃ muchakucha 'incoherence, confusion'
めちゃめちゃ mechamecha 'mess, ruin'
I also really like the sound of 熟字訓 jukujikun, which reminds me of the "chicka-chicka" in "Oh Yeah" by Yello.
It's also a fun word because it refers to something that only exists in Japanese: a kanji compound with a meaning based on those of the constituent kanji but a reading that does not relate directly to those individual kanji. (Examples here.)Another interesting word is 嫌煙権 ken'enken 'the right not to have to breathe second-hand smoke'. As a non-smoker, I appreciate the concept, and I love the fact that Japanese has a nice, compact word for it.
EDIT (2014.11.14): Here's a new favorite that I just recently learned: 積ん読 tsundoku 'the act of leaving a book unread after buying it, typically piled up together with other such unread books'. This one perfectly describes my life and my apartment.
What are other people's favorites?
