I came across situations where it looks like they don't pronounce the final letter of every word in a sentence? Personally, I feel that skipping the final letter somehow seems beautiful? What is the extent of correctness in my thought? Secondly, is it a good practice to do so? I would love to hear from native English speakers.
It's unclear what you mean by ‘every final letter’ (and I wouldn't say every letter is dropped), but I'll start off by classifying English accents into two main categories:
- Rhotic accents: Rhotic accents are ones in which the R is pronounced in all positions (red, park, car; the R in all these words is pronounced). Most American and Canadian accents are rhotic (there are also rhotic accents in Britain).
- Non-rhotic accents: Non-rhotic accents are ones where the R sound is only pronounced when it comes before a vowel sound (not the vowel letters a e I o u), so the R is pronounced in red, arrive, car is but not in bar, park, card etc. Most English-English accents are non-rhotic (there are also non-rhotic accents in the US such as New York and Boston). So the final (and pre-consonantal) R's in non-rhotic accents aren't pronounced.
Other consonants that are usually affected in speech include p, t, k. I wouldn't say they're dropped but rather ‘unreleased’. If you have noticed, p t k are produced by blocking the air at a particular place of articulation and then the blocked air is released:
- p is made by blocking the air at the lips
- t is made by blocking the air at the ridge just above the top teeth (called alveolar ridge)
- k is made by blocking the air at the velum (the soft palate)
Sometimes in word-final positions (and before certain other consonants), native speakers block the air for p t k and don't release it (= ‘unreleased’), so they can be inaudible.
There's another phenomenon called ‘glottalisation’ that happens to word-final (or syllable-final or pre-consonantal) t's in some accents (chiefly British). What happens is that the closure for the t (which is normally made at the ridge) is made in the glottis (= glottal stop).
Further, as pointed out in Graham's answer, the -ing in some accents such as Southern US, Cockney and AAVE is reduced to -in (i.e. from /ɪŋ/ to [ɪn]) so words like singing, going, morning are reduced to singin', goin', mornin'. That is called NG droppin'.
Incidentally, most (perhaps all) non-rhotic speakers usually insert consonants that are not present in spelling (ghost consonants!), for instance, [w] in go[w]away, [j] ('y') in he[j]is and (the striking) [ɹ] ('r') in saw[ɹ]a film or idea[ɹ]of. I've explained them in this answer to a question asking 'Is 'idea of' pronounced 'idearof'?'.
There are a number of regional British accents which do not do this, in a variety of ways. This basically applies to consonants which are omitted, altered, or replaced with a glottal stop.
Much of Britain will pronounce words ending with "ing" as "in"; so "I'm going out" becomes "I'm goin' out". (You'll often see it written this way in books too.)
For a number of regional accents too, the letter "T" is unvoiced, or replaced with a glottal stop if it occurs in the middle of a word or sentence. "R" is often also unvoiced too. So "Put your hat on" can become "Pu-ya ha'n". This is common for Essex, Liverpool and Scotland, although with different vowel sounds in each case for the relevant regional accent.
More than this, in much of Lancashire (north-west England) there is a tendency to simply not voice the end of sentences, and the last word trails off without being fully enunciated. I used to do this myself, and my first singing teacher had to do the whole "My fair lady" thing to get me to sound out the ends of sentences properly!
Just for a few examples...
Apart from words ending in r, there are not many English words where the last letter is a single silent consonant. Many of those come from other languages, for example ballet, valet. Some words have a consonant combination where only one is sounded, eg lamb, crumb, rock. The final consonant combination ng (as in running) represents a single sound and it is sometimes pronounced with a different sound, which would be spelt without the g.
The letter r, when not pronounced as a consonant, acts as a modifier for the preceding vowel. So while the final e in ride is not pronounced (though it modifies pronunciation of the i) it is pronounced (as some variation of er) in all accents.
In general it is much more common to pronounce the last consonant or consonant combination, than not. When speaking very quickly consonants may be reduced, as outlined in @Void's answer. Most people I know think that dropping consonants makes speech less beautiful, not more beautiful.