Q:

Origin of articles in European languages

I read that PIE, Latin, old English, and even old German did not use articles, yet current English, German and Romance languages all use articles.
Is it true that articles developed in all these languages independently from the word for "one"? What is the reason for their development? Were they useful in any way, such as helping pronunciation?

A:

Indefinite articles developed from numerals, and the definite articles developed from demonstratives. This is a very well known process called grammaticalization.

A:

Yes, this is true and yes, in most cases indefinite articles indeed developed from numerals, as @MGN already said. 
Not only there's no evidence of articles in PIE, the lack of articles is a more common phenomena than it can be expected to be from the Standard Average European point of view. Here's an interesting quote:

The geographical distribution of articles on a worldwide basis (WALS
  2005) confirms the Western European peculiarity: while languages
  lacking articles are common (out of 566 languages, only 188 have no
  definite or indefinite articles and 41 have no definite, but only
  indefinite articles), one area in which lack of definite article is
  infrequent is Western Europe.

Moreover, as it can be read in the article provided, the upcoming process of 
grammaticalization of articles can be observed nowadays in some Slavic languages.
Even more, there are some hypothesis that definite articles in some cases underwent further evolution and transformed to some other grammar units. For example, Joseph Greenberg claimed that this is how some languages acquired gender markers. 

A:

Articles in Macedonian are like demonstrative adjectives attached to the nouns, so there are 3 degrees of ''proximity'' observed.
My language (Croatian) does not have articles, but it has a concept of definite and indefinite adjectives:
dobar konj  = a good horse
dobri konj = the good horse
predicative:
konj je dobar = a/the horse is good
with numbers, you use definite adjective:
jedan dobri konj = one good horse
neki dobri konj = a/some good horse
because by putting an identifier (jedan=one, neki=some, a), you are making it more definite.

