I have read that verbs in Japanese are a closed class. That is to say: not counting inflections, there is some relatively fixed number of "true verbs" in the language. By "true verbs" I am excluding compound verbs formed with [noun]+する, or really [noun]+[verb] of any type. If this is the case, surely there is some estimate of roughly how many such verbs exist? I believe that i-adjectives are also a closed class, and I'd be curious about their number as well.
Coining new godan verbs (u-verbs) is far from exceptional in modern Japanese, and we have many related questions on this site.
- What are the principles behind turning foreign language words into verbs?(e.g. ググる and サボる)
- Characteristics of 'loan word root + る' verbs
- Can you form verbs from 擬態語 or 擬音語 by adding -る?
- Meaning and validity of 雪ってる
- What does ゴリってる mean?
- Pronunciation Troubles with トラブル and トラブる: Loanwords with both noun and verb ending in ru mora
I listed some well-known ones in the comment section, but just to support this, here are some rare u-verbs I happen to know personally:
- ジャムる: "to be jammed" (gun, military jargon)
- ばみる: "to use plastic tape to mark the positions of actors on stage" (actor's jargon)
- メタる: "to defeat an opponent with the aid of metagame" (card gamer's jargon)
- アポる: "to develop a brain infarction" (medical argot)
- サチる: "to saturate; to reach the limit" (data scientist's jargon)
- マミる: "to be decapitated" (anime fan's jargon)
- タヒる: "to die" (from the bottom part of 死)
- へごる: "to say something funny unintentionally" (Ayaka Ohashi's fan's jargon)
- ジュレる: "to be half-frozen" (leaves, gardening jargon)
Okay, these are used only in small communities, and I think less than 10% of native Japanese speakers know them. But I believe words like these are coined almost every day somewhere in Japan, and this is exactly why u-verbs are productive in Japanese.
On the other hand, the number of Japanese 助動詞 is relatively small and you can see the full list in Japanese Wikipedia.
Anyway, if you want a rough estimation, according to this page, the number of Japanese verbs listed in a certain dictionary is 10,265 (but this should include lexicalized compound verbs like 取り戻す). 国研日本語語彙DB recognizes 236 i-adjectives, but according to this page, the number of Japanese i-adjectives recognized by ATOK9 is much larger (1,302). 『品詞別日本文法講座4 形容詞・形容動詞』 by Suzuki et al lists 1,343 i-adjectives (and archaic precursors).
EDIT: I should've mentioned this... Ichidan (ru-) verbs are "relatively closed". According to this page, there are only 40 ichidan verbs that end with -iru (excluding compound verbs and archaic verbs).