Are articles in many languages such as English ("the") or French ("la/le") completely useless? How come many languages dont have articles?

They are not useless in a lot of languages.

For example in French, in many cases, the article is the only thing specifying the gender or number of a noun and if it can be quantified or not. It's even more obvious orally where there is no audible difference between the singular and plural form of most nouns.

It also makes the difference between the specific an the general.

For example, when you say "Danish people like Football", you don't actually know if you're talking about some Danish people or about all Danish people. In French, you know this because the article used is different (des and les).

But there are languages in which articles and prepositions are often not needed because there are other ways to indicate what I mentioned above. For example, in Latin, the form of a word indicated a lot of things about its function to the point that you could more or less chose a random word order and it would not change the meaning.

Note also, in addition to the many other fine answers, that Latin had no definite article at all, yet French, Italian, Spanish, Portuguese, and Romanian (among other languages that Latin evolved into) all have definite articles (which in many cases evolved from demonstrative determiners in Latin, meaning this/that/these/those), with new demonstrative determiners forming from other words.

Japanese, which has no definite or indefinite articles, nevertheless has an exhaustive particle, to indicate that the noun or pronoun is the sole satisfier of the predicate (very close to the concept of definiteness), and a topic particle which can indicate that there are other nouns that could satisfy the predicate as well (very close to indefiniteness), among other concepts.

Some languages have verbs that do not indicate tense at all, but they can still talk about the past, present, or future by using time words/phrases (among other ways). Tense is not useless in languages that have the concept.

It is similar with definite or indefinite articles.

They really aren't useless or they would have died out, like the others said.

Although in German in very informal situations (ie, conversing with friends) instead of worrying about der, die, das, some people just say 'de'.

It's not proper grammar or anything, and anyone listening on the outside likely thinks you are an idiot, but it's much easier then worrying about proper grammar.

if they were completely useless, they would have died out...

and even in languages that don't have articles, there are other subtle ways of indicating whether they're talking about a cat or the cat...

they really aren't useless or they would have died out, like the others said...

although in german in very informal situations (ie, conversing with friends) instead of worrying about der, die, das, some people just say 'de'...

it's not proper grammar or anything, and anyone listening on the outside likely thinks you are an idiot, but it's much easier then worrying about proper grammar...

No, they are not completely useless. They have many uses. Other languages use other linguistic means to accomplish the same purposes. Neither means is better or worse; just different.

In all the languages I know that have a definite article (English, German, Greek, French, Romanian, Portuguese, Spanish, Dutch), it is derived from the word for "that" or "this", and is used to particularize: "The man" is the one we both know, or the one I have been talking about etc. "Homo sum, nihil Mihi alienum puto": I am a man (just any man), "Ecce homo": behold the man (the one of especial importance), "Arma virumque cano" My poem is about weapons of war and the Man (Aeneas, my particular hero). "Fuit homo" There once was a man (never mentioned before).

no, they are not completely useless... they have numerous uses... other languages use other linguistic means to accomplish the same purposes... neither means is better or worse; just different...

You can have as many different meanings of one word as grammatical genders exist (very economic): Example (German): das Laute (neutral gender): the Noise, die Laute (female): the lute / the noisy woman; der Laute (masc.): the noisy man. "die Leiter": the ladder, der Leiter: the leader; die Steuer: the tax, das Steuer: the rudder; die Kiefer: the pine, der Kiefer: the jaw. der Otter: the otter, die Otter: the viper; das Tor: the gate, der Tor: the schmock.