user13207: I'm referring to translations in accesstoinsight.org; what is the word in Pali that is translated as "being" by John D. Ireland and "becoming" by Thanissaro Bhikkhu? For example, in Itivuttaka: The Group of Twos -  49. Held by Views.  links and sample translations are given below.
John D. Ireland translation 

"Bhikkhus, held by two kinds of views, some devas and human beings
  hold back and some overreach; only those with vision see.
"And how, bhikkhus, do some hold back? Devas and humans enjoy being,
  delight in being, are satisfied with being. When Dhamma is taught to
  them for the cessation of being, their minds do not enter into it or
  acquire confidence in it or settle upon it or become resolved upon it.
  Thus, bhikkhus, do some hold back.

Thanissaro Bhikkhu translation 

This was said by the Blessed One, said by the Arahant, so I have
  heard: "Overcome by two viewpoints, some human & divine beings adhere,
  other human & divine beings slip right past, while those with vision
  see.
"And how do some adhere? Human & divine beings enjoy becoming, delight
  in becoming, are satisfied with becoming. When the Dhamma is being
  taught for the sake of the cessation of becoming, their minds do not
  take to it, are not calmed by it, do not settle on it or become
  resolved on it. This is how some adhere.


user8157: The Pali word is 'bhava', which is defined in AN 3.76 as the mind 'established' (patiṭṭhitaṃ) in a sensual, material or immaterial element. For example, if the mind is stuck in delighting in the taste of delicious food, this is 'bhava'. 

Lord, this word, ‘becoming (bhavo), becoming (bhavo)’—to what extent is there becoming?
Kamma ripening (vepakkañca) in the sensuality-element.. is sensuality-becoming... 
Kamma ripening in the form-element... is  material-becoming...
Kamma ripening in the formless-element... is immaterial-becoming...
Thus kamma is the field, consciousness the seed and craving the moisture. The consciousness of beings (sattānaṃ) hindered by ignorance & fettered by craving is established in (patiṭṭhitaṃ) the sensuality... material ... immaterial element. Thus there is the production of new becoming in the future.
AN 3.76

'Bhava' is caused by 'craving' & 'attachment' and includes self-views: 

The craving that makes for further becoming (bhava) — accompanied by passion & delight, relishing now here & now there — i.e., craving for sensual pleasure, craving to be, craving not-to-be: This, friend Visakha, is the origination of self-identification described by the Blessed One.
MN 44

Most importantly, 'bhava' is a mental defilement (rather than the existence of life), as follows: 

Tayome, bhikkhave, āsavā— kāmāsavo, bhavāsavo, avijjāsavoavijjā
There are these three kinds of fermentations: the fermentation of sensuality, the fermentation of becoming, the fermentation of
  ignorance.
AN 6.63

Iti kāmayogo bhavayogo diṭṭhiyogo avijjāyogo, saṃyutto pāpakehi akusalehi dhammehidhamma saṃkilesikehi
Such are the bond of sensuality, the bond of bhava, the bond of views and the bond of ignorance. One is fettered by bad unwholesome states
  that are defiling....
AN 4.10

For him — thus knowing, thus seeing — the mind is released from the fermentation of sensuality, the fermentation of becoming (bhava), the fermentation of ignorance.
MN 121

The Blessed One has realized for himself with direct knowledge, in this very life, the fermentationless liberation of mind, liberation by wisdom, and having entered upon it, he dwells in it.
AN 10.30


user43: The word is "bhava" and in my understanding it refers to a particular state of individualized existence: "being a living being", "being a human", "being a person". So it's not about just the mathematical fact of existence, it is about your subjective position of identifying with this particular organism and its personal story, its narrative.
So when Buddha says "devas and humans enjoy being", and "Dhamma is taught for the cessation of being" - it does not mean, Dhamma advocates death or annihilation, it advocates transcending identification with an individual living being.
Does not mean Dharma advocates identitying with Universe  either, that's another wrong view. Instead, the right view is to see the unhealthy outcomes of any and all identification and to abandon identification altogether.
P.S.
As @ChrisW noted, bhava is also notably mentioned in the Second Noble truth as classification of tanha (craving) into bhava-taṇhā and vibhava-taṇhā. In that context, again, bhava refers to a particular sate of existence - in this case a state of existence that we crave for: "I want to live in a certain way, I want to be X, I want to be surrounded by Y, I want my life to look like Z". Vibhava then refers to not being in a particular state: "I want to stop being poor, I want to stop being sick, I want to stop being lonely" etc.
In all cases bhava seems to always be connected with an idea of self in a broad sense - self not as subject of experience or agent of actions, but rather as one's state of existence.

13207: <p>I'm referring to translations in accesstoinsight.org; what is the word in Pali that is translated as "being" by John D. Ireland and "becoming" by Thanissaro Bhikkhu? For example, in <em>Itivuttaka: The Group of Twos -  49. Held by Views.</em>  links and sample translations are given below.</p>

<p><a href="https://www.accesstoinsight.org/tipitaka/kn/iti/iti.2.042-049x.irel.html#iti-049" rel="nofollow noreferrer">John D. Ireland translation</a> </p>

<blockquote>
  <p>"Bhikkhus, held by two kinds of views, some devas and human beings
  hold back and some overreach; only those with vision see.</p>
  
  <p>"And how, bhikkhus, do some hold back? Devas and humans enjoy <strong>being</strong>,
  delight in being, are satisfied with being. When Dhamma is taught to
  them for the cessation of being, their minds do not enter into it or
  acquire confidence in it or settle upon it or become resolved upon it.
  Thus, bhikkhus, do some hold back.</p>
</blockquote>

<p><a href="https://www.accesstoinsight.org/tipitaka/kn/iti/iti.2.042-049x.irel.html#iti-049" rel="nofollow noreferrer">Thanissaro Bhikkhu translation</a> </p>

<blockquote>
  <p>This was said by the Blessed One, said by the Arahant, so I have
  heard: "Overcome by two viewpoints, some human &amp; divine beings adhere,
  other human &amp; divine beings slip right past, while those with vision
  see.</p>
  
  <p>"And how do some adhere? Human &amp; divine beings enjoy <strong>becoming</strong>, delight
  in becoming, are satisfied with becoming. When the Dhamma is being
  taught for the sake of the cessation of becoming, their minds do not
  take to it, are not calmed by it, do not settle on it or become
  resolved on it. This is how some adhere.</p>
</blockquote>
 8157: <p>The Pali word is 'bhava', which is defined in <a href="https://www.accesstoinsight.org/tipitaka/an/an03/an03.076.than.html" rel="nofollow noreferrer">AN 3.76</a> as the mind 'established' (patiṭṭhitaṃ) in a sensual, material or immaterial element. For example, if the mind is stuck in delighting in the taste of delicious food, this is 'bhava'. </p>

<blockquote>
  <p><em>Lord, this word, ‘becoming (bhavo), becoming (bhavo)’—to what extent is there becoming?</em></p>
  
  <p><strong><em>Kamma ripening</strong> (vepakkañca) in the sensuality-element.. is sensuality-becoming...</em> </p>
  
  <p><em>Kamma ripening in the form-element... is  material-becoming...</em></p>
  
  <p><em>Kamma ripening in the formless-element... is immaterial-becoming...</em></p>
  
  <p><em>Thus kamma is the field, consciousness the seed and craving the moisture. The consciousness of beings (sattānaṃ) hindered by ignorance &amp; fettered by craving is <strong>established</strong> in (patiṭṭhitaṃ) the sensuality... material ... immaterial element. Thus there is the production of new becoming in the future.</em></p>
  
  <p><em>AN 3.76</em></p>
</blockquote>

<p>'Bhava' is caused by 'craving' &amp; 'attachment' and includes self-views: </p>

<blockquote>
  <p><em>The craving that makes for further becoming (bhava) — accompanied by passion &amp; delight, relishing now here &amp; now there — i.e., craving for sensual pleasure, craving to be, craving not-to-be: This, friend Visakha, is the origination of <strong>self-identification</strong> described by the Blessed One.</em></p>
  
  <p><em>MN 44</em></p>
</blockquote>

<p>Most importantly, 'bhava' is a mental defilement (rather than the existence of life), as follows: </p>

<blockquote>
  <p><em>Tayome, bhikkhave, āsavā— kāmāsavo, bhavāsavo, avijjāsavoavijjā</em></p>
  
  <p><em>There are these three kinds of fermentations: the fermentation of sensuality, the <strong>fermentation</strong> of becoming, the fermentation of
  ignorance.</em></p>
  
  <p><em>AN 6.63</em></p>
  
  <hr>
  
  <p><em>Iti kāmayogo bhavayogo diṭṭhiyogo avijjāyogo, saṃyutto pāpakehi akusalehi dhammehidhamma saṃkilesikehi</em></p>
  
  <p><em>Such are the bond of sensuality, the bond of bhava, the bond of views and the bond of ignorance. One is fettered by bad unwholesome states
  that are defiling....</em></p>
  
  <p><em>AN 4.10</em></p>
  
  <hr>
  
  <p><em>For him — thus knowing, thus seeing — the mind is released from the fermentation of sensuality, the fermentation of becoming (bhava), the fermentation of ignorance.</em></p>
  
  <p><em>MN 121</em></p>
  
  <hr>
  
  <p><em>The Blessed One has realized for himself with direct knowledge, in this very life, the fermentationless liberation of mind, liberation by wisdom, and having entered upon it, he dwells in it.</em></p>
  
  <p><em>AN 10.30</em></p>
</blockquote>
 43: <p>The word is "bhava" and in my understanding it refers to a particular state of individualized existence: "being a living being", "being a human", "being a person". So it's not about just the mathematical fact of existence, it is about your subjective position of identifying with this particular organism and its personal story, its narrative.</p>

<p>So when Buddha says "devas and humans enjoy being", and "Dhamma is taught for the cessation of being" - it does not mean, Dhamma advocates death or annihilation, it advocates transcending identification with an individual living being.</p>

<p>Does not mean Dharma advocates identitying with Universe  either, that's another wrong view. Instead, the right view is to see the unhealthy outcomes of any and all identification and to abandon identification altogether.</p>

<p>P.S.</p>

<p>As @ChrisW noted, <em>bhava</em> is also notably mentioned in the Second Noble truth as classification of tanha (craving) into bhava-taṇhā and vibhava-taṇhā. In that context, again, bhava refers to a particular sate of existence - in this case a state of existence that we crave for: "I want to live in a certain way, I want to be X, I want to be surrounded by Y, I want my life to look like Z". Vibhava then refers to <em>not being</em> in a particular state: "I want to stop being poor, I want to stop being sick, I want to stop being lonely" etc.</p>

<p>In all cases <em>bhava</em> seems to always be connected with an idea of self in a broad sense - self not as subject of experience or agent of actions, but rather as one's state of existence.</p>
