What are The Buddha's most compassionate acts?

One story has the Buddha in a previous life crossing a river on a ferry. The passengers are attacked by a murderous thief and the Buddha kills him, accepting the karmic consequences. It may be a teaching story rather than an historical account but it would be an example of a compassionate act.

Almost each and every single act's of The Buddha is compassionate act's.

To accept the request to teach the Dhamma althought he neither had any duty to do so nor could see many who would accept his gift and take it to heart, put it into practice and to return so many, many times approaching his "worthless" disciples again and again.

Actually it's a question which needs requires to understand, that there is no action of a Buddha/Arahat, which is not perfect in compassion/wisdom and judgement of which in particular, would be leaded for the most by personal preoccupations and benefits for worldly desires and attachments.

Again, as possible known, the gift of Dhamma (showing the path to the deathless), excel all other gifts.

Of what counts as compassion/wisdom as foundation for actions is mentioned and declared as right resolve and only then without stains, if based on right view.

A person not having reached the path, a worldling, is not capable to see and understand real compassion, would always praise Maras actions as most compassionate. Only for one having accessed the Noble Domain, right resolve and compassionate actions (virtue section), is penetrated and understood. Only if actions are harmless for one self and all others is it right to speak about compassion and not just another act based on personal preference.

It is in dependence on me as an admirable friend that beings subject to birth have gained release from birth, that beings subject to aging have gained release from aging, that beings subject to death have gained release from death, that beings subject to sorrow, lamentation, pain, distress, & despair have gained release from sorrow, lamentation, pain, distress, & despair. ...admirable beings

I particularly enjoy his compassionate ability to encourage people to experience their own learning of dharma.

There is a lovely example here of his compassion in the story of the mustard seed and the death of a woman's baby.

https://www.accesstoinsight.org/noncanon/comy/thiga-10-01-ao0.html

In the Shurangama sutta also, the Buddha skillfully guides Ananda into searching for the six senses.

Excerpt from the Shurangama sutta:

"Ánanda, all phenomena, near and far, have their own nature.  Although each is distinctly different, they are seen with the same pure essence of seeing.  Thus all the categories of phenomena have their individual distinctions, but the seeing-nature has no differences.  That essential wonderful brightness is most certainly your seeing-nature. "If seeing were a phenomenon, then you should also be able to see my seeing. "If we both looked at the same phenomenon, you would also be seeing my seeing. Then, when I’m not seeing, why can’t you see my not seeing? "If you could see my not-seeing, it clearly would not be the phenomenon that I am not seeing.  If you cannot not see my ‘not seeing’, then it is clearly not a phenomenon. How could it not be you? Besides that, if you’re seeing of phenomena was like that then when you saw things, things should also see you.  With substance and nature mixed together, you, I, and everyone in the world would no longer be distinguishable from each other. "Ánanda, when you see, it is you who sees, not me.  The seeing-nature pervades everywhere; whose is it if it is not yours? "Why do you have doubts about your own true-nature and come to me seeking verification, thinking your nature is not true?"

Source: http://buddhasutra.com/files/shurangama_sutra.htm

Probably the decision to become a samma sambuddha for the benifit of others. Becoming an arahath and ending your own suffering is lot more easier and take lot less time.

“Then I listened to the Brahmā’s pleading, and out of compassion for beings I surveyed the world with the eye of a Buddha. Surveying the world with the eye of a Buddha, I saw beings with little dust in their eyes and with much dust in their eyes, with keen faculties and with dull faculties, with good qualities and with bad qualities, easy to teach and hard to teach, and some who dwelt seeing fear and blame in the other world. Just as in a pond of blue or red or white lotuses, some lotuses that are born and grow in the water thrive immersed in the water without rising out of it, and some other lotuses that are born and grow in the water rest on the water’s surface, and some other lotuses that are born and grow in the water rise out of the water and stand clear, unwetted by it; so too, surveying the world with the eye of a Buddha, I saw beings with little dust in their eyes and with much dust in their eyes, with keen faculties and with dull faculties, with good qualities and with bad qualities, easy to teach and hard to teach, and some who dwelt seeing fear and blame in the other world. Then I replied to the Brahmā Sahampati in stanzas:

‘Open for them are the doors to the Deathless, Let those with ears now show their faith. Thinking it would be troublesome, O Brahmā, I did not speak the Dhamma subtle and sublime.’ MN26