I know plenty of Japanese words that came from English and a few from other European languages (obviously tons from Chinese), but what about words from Japan's indigenous languages such as Ainu? Also if there are any are they all written in kana like the newer borrowed words?
Most Ainu loanwords in regular use are names for plants/animals indigenous to northern Japan, such as reindeer (トナカイ) and sea otter (ラッコ). These loans are old enough that there are usually kanji that can be used for them:
- 馴鹿 (トナカイ, also read じゅんろく)
- 海獺 or 猟虎 (ラッコ)
However, many plant/animal names are usually written in katakana in everyday use (e.g. カバ for "hippopotamus," though it can be written 河馬). Due to the Ainu words being borrowed so long ago and the fact that many people don't realize they aren't "native" Japanese words, I suspect they are usually written in katakana because of this convention.
I've read in at least a few sources that the word さる "monkey" is from Ainu sar'ush, literally "having a tail." Can't promise it's not a false cognate though. It's treated as a native Japanese word in writing.
Using katakana for loanwords was not common practice until after the Meiji restoration (older loans like コーヒー and ガラス can actually be written in kanji, although they generally aren't; たばこ is still written in hiragana).
Aside from that, many place names especially in northern Japan are derived from Ainu. "Sapporo" from Sat-poro-pet and "Shiretoko" from Sir-etok are two off the top of my head. These are generally written in kanji.
There are some words in Japanese which were borrowed from the Ainu language, and mostly, they are written in katakana. However, they are mostly very uncommon words. Likely one of the most common is ラッコ (sea otter) -- I don't know that there is another word for it. Another which you have potentially heard is カムイ, which is analogous to the Japanese 神（かみ）.
There may also be words borrowed from the language(s?) of the Ryukyu Islands (e.g. Okinawa), but I am not aware of any specific examples. If there are, they are also likely written (at least mostly) in katakana.
Here is a list of all words of Ainu origin listed as such in 大辞林
Many of Hokkaido toponymos (and even some on Honshu) are coming from Ainu language. It includes the such common ones like 札幌、 小樽 or 石狩.
I don't know this for sure, but I believe the word "Kanata" meaning roughly "far away" in Japanese may have come from the Ainu, based on it's homonym by Native Americans, who descended from the Ainu.