In my groups we have a few people who like to roleplay an accent for their character(s), or in the case of the DM, the NPCs we encounter.
As an aspiring voice actor(don't know why it's relevant, I just felt like sharing), I've often wondered what real world languages the in-game languages would sound like. For example: Dwarves are often portrayed as Irish/Scottish, so I would guess Dwarvish sounds like Gaelic.
What are some other comparisons that could be made, whether racial or language in terms of accents?
I'll make a list below and update it with suggestions as I get them.
Languages
Dwarvish - Gaelic
Elvish
Giant
Gnomish
Goblin
Halfling
Orc
Abyssal
Celestial - Latin
Draconic
Deep Speech
Infernal
Ignan
Auran
Terran
Aquan
Sylvan
Undercommon
Races
Dwarf - Scottish, Irish
Dragonborn
Elf - Haughty, English(as in England)
Halfling
Half-orc
Half-elf
Gnome
Tiefling - German?
Genasi
Aarakocra - Shrill
Goliath - Russian?
Orc - Cockney
Goblin
Dragon
Giant
I played a dwarf recently with a burly russian-ish accent and everyone thought it worked out quite well.
I see halflings as having a combination of light english and southern american accents. or maybe even a light australian accent
dragonborn and tiefling I could both see as having a sort of middle eastern accent like arabic or turkish, or spanish
generally orcs are portrayed with a rough low british
just because someone needs to be french, i could see gnomes as french easily.
i dunno
I've always imagined Drow as having a lispy Castilian Spanish sound. If nothing else, it deters players from wanting to be Drow.
Genasi ought to have a Middle Eastern accent, if we're playing to tropes.
Halflings NPCs get something like an upper Midwest/Canadian treatment at my table.
I use a Russian accent when I speak in Infernal.
This is because WotC did a promo for 4th edition where a Gnome was interviewing a Tiefling, and the Tiefling spoke with a Russian accent. 
Infernal is the language Tieflings know, therefore Inferal must be Russian! 
If High Elves get City-of-London British accents ( = the Queen), then
Wood Elves could be Scottish (Sean Connery as James Bond)
Half-Elves get to be working-class Irish or Cockney
Halflings are supposed to be based on 'typical countryside Englishmen', so give them that accent because it makes them sound polite and good-natured.
I've always thought of Draconic as the language magic spells are spoken in, so like Latin;
Dragons themselves should have a booming baritone / bass, depending on just how big they are.
Abyssal and Infernal ought to sound like much cursing and swearing - even when you're not.
Terran should be done in a gravelly voice, pardon the pun,
Aquan-speakers sound 'wet' like waves rolling up on a beach,
Auran should be light and breathy,
Ignan should have a lot of pops and sizzles and hisses in it.
I could see an Orc that sounds like Sean Connery (Scottish) trying to do Russian, as in Hunt for Red October.
But I really see an orc speaking in Godfather-style Mafioso-American.
If you look at the race in the PHB for some of them they give you a description of the "accent" for example.
PHB wrote:
Could Draconic sound like Arabic?
Elvish could be French.
Gnomish could be Italian, being similar to French in some ways.
Abyssal would probably sound like death metal. Spoken from the bowels of the lungs.
Deep Speech could be Spanish. FG wiki give the word zin-carla as an example.
I want Xhosa (African clicking language) to be similar to some fantasy language. I just don't know which.
Oftentimes, all you need for an 'accent' is to change a speech pattern, slow down how fast you talk, or never use any contractions... that kind of thing. It will make you sound 'foreign'....