Ten temples might be too many to think of right now, but the title had a nice ring to it and there really are SO many temples, that it does help to get personal opinions on which ones are worth seeing in a limited amount of time.

    Kiyomizu - I would definitely recommend. In Eastern Kyoto it stands far apart from the many others temples you'll see in Japan. Upon a hillside overlooking Kyoto, the temple has a wonderful view of the city. Even the massive wooden pillars supporting the temple have a certain charm, (I think the entire temple might have been built without nails). Sip water from the special flowing spring as you leave the temple for blessings of fortune and health. But the real must is walking down the picturesque Ninnenzaka as it leads away from the temple. A great place to stop and have a snack is Kasagi-ya a tiny homey tea shop with only a handful of tables, but which serves the best ohagi and tea sweets I've ever had. Their Kaki-gori (shaved ice) with green tea is also so oishii you'll want to make the trip back to Kyoto just for this little shop. (if I remember correctly if you're walking down the stairs of Ninnenzaka it's on the left hand side, partially covered by the stairs - look for the kaki-gori kanji)

    Todai-ji - if you have the time this is a nice day trip from Kyoto (it does take the whole day though, so only if you have the time). Todai-ji is memorable from other temples just for the sheer massiveness of the Buddha. The bowing deer and being pulled through a hole in the pillar (the size of the Buddha's nostril) for good luck, makes it even more enjoyable. Watch your pockets though, the deer can get a little aggressive.

    Kinkaku-ji - SO different from any other temple. GOLD. Not quite what I think of when I think of the tranquility and peace of zen gardens (and personally, I think I prefer the calm of Ryoanji or Ginkakuji) but if I were never able to visit Kyoto again in my life, then this is something I would have wanted to see.

    Okay, so sorry to disappoint. I'm stopping at three. ;) Just wanted to put in my couple of two cents on Kyoto temples to balance out Kai.  :D