Sure, I’ll go into a bit more detail:
- ある - to be (to exist)
- 上がる - to be raised
- 下がる - to be lowered
- 分かる - to be understood
- 代わる - to be replaced
- 止まる - to stop
- 当たる - to be hit / to be (correctly) guessed
- 回る - to turn
- 決まる - to be decided
- 助かる - to be helped / to be saved
- 終わる - to become finished
- 転がる - to fall (over)
These verbs are all intransitive, just like ある, which means that these verbs do not (cannot) take the particle を. This is because they are actions that the “subject” of the sentence (which is prescriptively marked by が, but may be specified by は, or else omitted entirely and left implied in Japanese) simply does on its own, without any transitive “target” (“direct object,” marked by を).
In direct contrast to that, this list here…
- する - to do (something)
- 出す - to take out / put out (something)
- 正す - to correct (something)
- 写す - to duplicate / imitate (something)
- 申す - to humbly say (something)
- 足す - to add (something)
- 直す - to fix (something)
- 回す - to turn (something)
- 思い出す - to remember (something)
- 見直す - to re-examine (something)
- 話す - to narrate / discuss / tell (something)
- 欠かす - to miss / fail doing (something)
- 表す - to represent / reveal / express (something)
- 返す - to return (something)
- 通す - to allow (someone / something) to pass
…is entirely transitive, like する is. It’s understood that for each of these verbs, [ _____を] is a part of the sentence. For example, 宿題を出してください means “please hand in (your) homework,” and even if you leave out 宿題を, it would still mean “please hand (it) in” because the fact that 出す is transitive means that something absolutely must be the “direct object” of the phrase, even if we leave it unsaid.
Here are a few more examples of how transitivity is understood, and what can happen if you use it incorrectly. 開く (あく) and 開ける (あける) here both mean “to open,” but 開く is intransitive and 開ける is transitive:
Correct:
○ ドアが開く。 → “The door opens.” (nothing is implied)
○ ドアを開ける。→ “(I / we) open the door.” (the sentence’s “subject” is implied)
○ 私(は・が)ドアを開ける。→ “I open the door.” (nothing is implied)
○ 私(は・が)開ける。 → “I open (the door).” / “I open (it).” (the sentence’s “direct object” is implied)
Incorrect:
× ドアを開く。 → This is like saying “fall the ball,” “rise your hand,” or “die the enemy”
× ドアが開ける。→ Technically, this is grammatically correct, but it’s strange since it’s saying “the door opens (something),” with (something) being implied since we haven’t specified what’s being opened (because we have no を in the sentence)
Note:
ドアが開ける would actually probably be read as ドアがひらける, which would even be normal / natural since ひらける is intransitive, but that’s more of an issue of there being too many verbs using the 開 kanji than anything else 
A beginner mistakenly saying「ドアがあける」instead of「ドアをあける」or「ドアがあく」would still be strange. EDIT: Or, it could be interpreted as the potential of 開く, which would make the sentence mean “The door can be opened / is openable” instead of “the door opens.”