I was thinking of trying to make language more fun or useful, and what I thought was this: what if you got rid of Common altogether? 

I mean, we've all played characters with bonus languages we've been excited about, but only ever use like once or twice. Imagine if Common wasn't a thing, and the languages you picked had a much bigger impact on how you played the game? And characters with high intelligence getting to pick extra languages would get a lot more utility out of what is usually a dump stat for all non-wizards.

Certain languages would still be considered "common" for certain areas, based on geography or ethnic makeup, so I can see like, a human living in a predominately elvish nation growing up speaking elvish and "human." I feel like this would give it that much more of a real world feel if the story has them interacting with enemies with other nations who can't be so easily parlayed with, and would be particularly rewarding if a character happened to have the right language for a situation. Or it could be cool/ hilarious trying to negotiate a frought situation with a hostile party where neither spoke each other's languages, trying to convey terms through mime or other creative solutions. 

Do you think this could be fun, or do you think whatever "common" geographical language would just replace Common ultimately for simplicity's sake? 

D&D is odd when it comes to languages (it is something they "patched" onto the rule set over the years), so I think you have to "homebrew" yourself.

1. How much "prime material plane" driven will your campaign be?
With languages like Abyssal or Celestial being available at character creation (RAW), will they ever see any use or make sense (why does a person with an angelic bloodline speak the tongue of angels? It is like "I have an Italian grandfather, I can speak Italian"). Should you focus on very little dimension/planar travel, you might want to switch them out.

2. Will "racial languages" create language barriers, or will geography/politics create them?
If you forgo the concept of racial languages (e.g. we don't have "Caucasian" or "Asian" as a language in real life), you can introduce geographic languages, like "Zemnian", the language spoken in the "Zemnian Empire" (where everyone speaks that language, with no distinction of race).

3. Old and contemporary languages?
Will some languages be considered out of use (like Latin), but still relevant (e.g. because of manuscripts and books) and others considered "common" (like English)?

4. Are you willing to transfer Languages to the skill system?
If you are giving conversations in a language (or reading books) skill checks, you gain a lot more flexibility and in-game value for the languages. it will require some work, though.

Example:

Everyone starts with a revised "Common" language. They are always proficient with that language and might be allowed to add a proficiency bonus to that checks (see below).
==> "Common" will be "Zemnian (Int)" they language of the region the players start in.
Racial languages will be treated as "Common", but without the proficiency bonus (e.g. "Xhorhasian (Int)") and give you access to another regional language as their "secondary language".
Outer plane languages (Celestial, Abyssal) will be treated as an "ancient language", which will be uncommon to most of the inhabitants of the game world.

Brugar (Dwarf, Fighter) and his brother Horgar (Dwarf, Wizard) are "created" (Lvl 1).

Brugar choses "Zemnian" and adds his "Int" bonus (+0) and his proficiency bonus (+2) to a roll. Instead of having "Dwarven" he gets "Xhorhasian", because he has served in a mercenary company that had a lot of people from the Xhorhasian Empire among their ranks, too. His background (soldier) does not give him an additional language.
Horgar is more proficient in languages than is brother: Zemnian (Int) = +3 from his Intelligence, +2 from the proficiency bonus (total +5); he also speaks "Ancient Dwarven" and due to his Acolyte background "Celestial" and "The Tongue of the Trader's Coast". Because he comes from a "knowledge/diplomatic" character class ("homebrew" content coming up) the DM allows him to add his proficiency bonus to a second language.
Players in this campaign will be allowed to speak two more languages than they had after character creation and will get a chance to improve their languages whenever they hit an "ASI stage". A known language could be improved to proficient use, or a new language can be learned. "knowledge/diplomatic" character classes (I would say Bard, Wizard, Cleric, Monk, Sorcerer), also have the option to gain "expertise" in a language they are already proficient in and they can learn as many languages as the other classes + their Int modifier.

At Level 5 ("ASI spot" has been noted at lvl 4) they have spent most of their time adventuring at the Menagerie Coast. Brugar picks up "The Tongue of the Trader's Coast" as a third language at lvl 4. He roll "Zemnian" with a +3 bonus (due to his raised proficiency bonus now) and "The Tongue of the Trader's Coast" + "Xhorhasian" with no bonus. He can learn one more language in the future.
Horgar has chosen to improve his "The Tongue of the Trader's Coast" to a proficient roll at level 4. For his language skills, he now rolls:
"Zemnian" and "The Tongue of the Trader's Coast" with a +6 bonus and "Ancient Dwarven" and "Celestial" with a +3 bonus. He has the potential to learn 5 more languages in the future (+2 on his original languages + 3 from his Int modifier).

I like this idea. I might ask my players about it. Thanks:)!!!!

This makes sense to me.  It would certainly make the Intelligence stat or having a Ranger more valuable overall.  

I put up a thread a month or two ago about reading and writing, basically how it was strange that every PC is assumed to know how to read and write in at least one language.  You might want to read it to get some more ideas.   

This is one of those things the game glosses over for the sake of simplicity and playability.  I don't see a lot of benefit to changing it.

personally i think the idea has merit, but like you said human/common would have variations that would cross over to other races i would think, ie thieves cant universal for all thieves regardless of race... 

It really depends on the scope of the world and WHY you want to do it.  If it is to make it "more realistic", well, that doesn't really work that well.  For any "high level" negotiations a Comprehend Languages ritual will ALWAYS be performed and you are back to having Common.  If it is to create a social challenge, the same can be done using different races which do not speak Common, and is overcome in the same ways as if the Party does not know a language.

If the scope of the campaign world is small (Like the size of Britain (the island)) then one can have Common with accents, which can lead to "misunderstandings" and roleplay opportunities without getting into minutia.   If the scope of the campaign world is big (like Europe) then it makes sense to have multiple languages, but it also makes sense that learned folk will know more than one language, at least spoken if not written.  If the scope is massive (like Earth) then it gets down to language families, and normal learned folk only knowing languages in their family or neighboring realms.  Specialists would be able to learn far flung and rare languages.  

The number of mechanics one can use to implement this is virtually unlimited. I generally don't think Barbarians or Druids should be able to read or write.  Substantial deviation from average Intelligence may also inhibit reading/writing.  An Intelligence of 8 or more would most likely be able to read and write though.  Remember 8-12 would be the normal range for society in any stat.

A good overall compromise is to have a "Trader's Tongue" which would have some universal symbols and an abbreviated word/phrase count which would pretty much allow anyone to get a meal, get a bed, which way to a known place, and how much (point at item)?  Image the symbols to be akin to Visa/Mastercard taken here on the doors of modern places of business.

For purposes of realism, this is a great idea. However, game play isn't always about realism. I'm not sure having to manage language proficiencies in order to be able to communicate is going to be fun for most people.

I think that if you wanted to play up the usefulness of secondary languages, then treat it you might see languages used in ethnic enclaves in major North American cities: everyone speaks "common" ( English ), but they have their own language which they drop into when they want semi-private, semi-covert communications between each other. If you've ever watched YouTube videos like "clueless looking white guy shocks restaurant owner with flawless Mandarin", you'll see what I mean :)

Making languages "fun and useful" really is a GM responsibility. Have the NPCs make side comments to each other in a non-common language ( NCL ). Use NCLs in written documents. Use NCLs in your naming conventions for people and places. 

Use NCLs as a spice, used for variety, to mask secondary clues to the adventure ( information which makes solving it easier, but isn't required to solve it ),  and to set an atmosphere, rather than as a core mechanic that the Players have to juggle on top of everything else for basic communication.

In short, if you make NCLs a useful ( but not essential ) part of a living, vibrant, dynamic campaign setting, the Players will pay more attention to them, and use them more.