are there language(s) without a doer?

Oh yes. English drops the subject all the time. We just do it in ways that maintain the basic SVO grammar. For example:

My friend came and ate.
My friend who is eating came.

However, in independent clauses, we usually maintain the SVO even though there is no logical reason to do so:

It’s raining.
It’s Monday.
It’s 9:00.

In your example, it would be perfectly normal if the periods were replaced with commas.

Aren’t there simpler examples of subjectless sentences in English?

“Go.”
“Run.”
“Drop dead.”
“Help me.”

All imply the you without saying it.

Or am I misunderstanding the concept?

Those examples aren’t classified as sentences. There’s several classes of phrases that do not follow sentence-level grammar:

Exclamations: help, ow, arrgh, etc.
Interruptions: Excuse me, pardon, one sec, etc.
Commands: Do it, get out, leave me alone, etc.
Space fillers (brain fart on the technical term): Um, ah, er, etc.
Rejoinders: Aha, I see, That’s great, That’s too bad, etc.
Stand-alone prepositional phrases: In the morning, at night, etc.
Politeness markers: Please, thank you, you’re welcome, etc.

In regards to the OP, the “doer” (aka the subject of the sentence) usually can’t be dropped at the sentence level in English, especially if it is at the beginning of the sentence. One exception is the passive construction (be + verb + by) where it is common to drop the actual doer of the verb:

It was built (by Romans) in 100 B.C.

But notice that it still must have a subject of the sentence.

An imperative is not a sentence? An exclamation is not a sentence? Says who?

A command isn’t considered a sentence? If I say something like “Go to the store and buy some hamburger for supper tonight and check to see if we’ve got cheese and rolls and get some if we’re out” that’s not a sentence? There’s a fair amount of specific information being conveyed there.

As sentences in the sense of needing SVO order.

Amount of information doesn’t matter.

I am hungry because I was surfing all day starting at 10am until 12pm and I didn’t have a chance to make lunch and when I went to McDonalds I realized I had forgotten my wallet.

By removing “I am hungry” the entire “because” clause becomes a dependent clause and is not a sentence.

Well, in the imperative mood in English, the subject is implied. Regardless, it’s grammatically a sentence any way you slice it.

I’m not a linguist and I don’t know whether there is a language with EXCLUSIVELY no doer.

But probably most languages allow for the possibly of either no subject or no object, usually in English labelled as either passive or active voice:

No doer (subject): The soap was picked up.

No doee (object): Joseph ran.

I know that the constructed language Klingon (was it modeled on a real life language??) has no verb “to be” (which caused issues when they had to translate the play Hamlet and it’s “to be or not to be”…).

In general, more sophisticated languages allow for greater variability of expression…

Again, we should distinguish between the syntactical notion of subject/object and the semantic notion of agent/patient. The “doer” is the agent, the “doee” is the patient.
But the subject can be both agent and patient (examples from Section 2 of http://www.eskimo.com/~ram/lexical_semantics.html):

The man obeyed the rules - the rules do not experience the man obeying them, he does. So the man is both agent and patient. “The rules” is the object of the verb, but its semantic role is the theme, or topic, or “focus” as the article above calls it.

And there are also examples of agentless verbs in which the subject is the patient, typically verbs involving unconscious or involuntary acts:

The candle melted
The book lacks a cover
The girls hear the music (compare to The girls listen to the music, in which the subject is the agent).

When words are dropped from a sentence and it does not affect the meaning, the term for that is understood. In the examples above of imperative sentences, the subject you is understood.

This article lists many languages that drop the subject of sentences in many cases where the subject is understood:

None of the languages mentioned though drop the subject in all cases.

It’s hard to believe that there are languages that express the idea “I was walking” as “There was walking” all the time. How would such a language distinguish between “I was walking,” “You were walking,” “Joe was walking,” “A tall man with dark hair was walking,” etc.?

It may be possible that there are languages which don’t have subjects (although I’ve never heard of such) that express such sentences as “There was walking for me” or some such. That’s not a case of not expressing a do-er (i.e., an agent) though. I don’t think there are any languages in which one can’t express the idea of an agent.

In both of those examples the subject is ellided; in MeanOldLady’s example, it’s a reflexive verb where the glass acts as the subject and is, in fact, present (“se rompió el vaso”, “se me cayó el vaso”). Different construction altogether.

Another construction which can be confusing in Spanish is impersonals. “Llovía” - “(it) rained”; who rained? Nobody. But, again, it’s used only in specific cases.

I am (very) far from a language expert but some of these examples remind me of pidgen/creole constructs that I’ve read about. Are there any pidgen languages that come close to meeting the OP’s criteria?

I don’t think so, although I don’t really know for sure. I’ve read that pidgin languages tend overwhelmingly to have SVO (subject-verb-object) orders. This would seem to imply that they always have subjects in their basic sentences, although there may occasionally be understood subjects in some sentences.

There seem to be answers to more than one question here. Does the OP wish to know:

[li]If there is a language without grammatical Subject?[/li][li]If there is a language without any means of expressing agent?[/li][li]If there is a language in which an impersonal agent is understood as referring to a person?[/li][li]Is there a language in which you can omit mentioning the agent, and it’s understood?[/li]
Obviously, the last one is a ‘yes,’ but is that what the question is about? And of course I’m sure many languages allow an impersonal agent where asking what was doing the action of the verb is absurd, such as “It rains” in English or “Pluit” in Latin.

As far as Spanish and Japanese, I wouldn’t get so caught up in splitting up words by the spaces in the orthography. You should be looking at morphemes, not words. Otherwise, all the highly agglutinative languages would qualify as “subject-less” when it really ain’t so. And you’d have an even greater problem with the fusional languages. Take Spanish, for example. “Te llamo” has a subject. It’s the “o” on the end. It’s just not a separate word and it’s been fused with other meanings, like “singular” and “indicative”.

Once again, I’m not a Japanese speaker, but doesn’t Japanese only conjugate according to tense, so there is no grammatical information indicating person/number/gender/etc?

I’m only learning Japanese, but you’re right. Japanese verbs only conjugate according to tense, politeness, and negativity. (well, and active/passive/causative/conditional/etc.)

Unlike Spanish, Japanese verbs don’t contain any clues as to the identity of their subjects.