Let me see... almost everyone you see are mostly Spacers and Colonists so their accents tend to be mixed and unreliable to show they actually came from Earth.
Shepard have a slight Canadian accent especially in ME3, thanks to their VAs but I'm not convinced Earthborn is a Canadian. The background came with "an orphan raised on the streets of the great megatropolises covering Earth." which I imagined overcrowded 'third-world' megacities with slums than the rich utopia-like large and open megacities in Alliance-based countries like Vancouver and London. Also shouldn't accent be affected by a person's socioeconomic status? But I like Shepard's ambiguity so.. I'll let this rest.
Kaidan was born in Singapore and raised in Vancouver. Someone mentioned he's probably Eastern European by decent especially with his last name.
Ashley was a Colonist but as with Spacer Shepard who have military background, she didn't stick around too much. I thought her accent was generic American English.
As for Anderson... frankly, I'm not that surprised with British people speaking in non-British accent. I've seen John Barrowman with American accent and yet he is a proud Scotsman. He got teased/bullied as a kid about his accent and he worked hard to sound 'normal', he still lapse sometimes. Anderson probably have a heavy South London accent which people tease about so he might have changed them to be respectable. (another example, James Boyega in Attack The Block and then watch him again in Force Awakens)
According to the novels, Kahlee was from Texas.
Chakwas came from a long line of doctors but I think she's the only one who went military. I think she's a spacer considering she prefer being in spaceships and travelling than she does staying in one place. I thought her accent was quite RP-ish (but not as bad as Jennifer Hale in KOTOR).
Ken mentioned repetitively that he's a Scot but I know actual Scots players would argue that his Scottish accent is weird. I thought Fitz in Agents of SHIELD is an improved version of Ken although Iain play him with a tone down Glasgwegian accent while Ken's VA play it him in some kind of exaggeration?
I think there's a good discussion about Zaeed's mixed accent.
Vega was based on Freddie Prinze Jr, so he's a Californian of Puerto Rican decent. Whether his Spanish was correct is debatable but I thought it add to his charms.
Kasumi is a Spacer of Japanese descent.
Samesh Bhatia in ME1 is of Indian descent although Brian George himself is a British-Israeli of Iraqi-descent who is famous for portraying South Asians and he voiced Oleg Petrovsky who is Eastern European.
Khalisah Bint Sinan al-Jailani is Arab or at least Middle Eastern. Her name follows standard Arabic patronymics, I'm certain al-Jailani is her grandfather or clan name. I think she's from Earth.
Yvonne is from Sydney and she uses her natural accent for Miranda. But Miranda is a spacer and she probably pick up the accent from her father.
TIM is Martin Sheen. American.
Bailey is Micheal Hogan. Canadian.
Jacob is probably a spacer. In the games and comics, he seemed to be more comfortable drifting around rather than sticking to one place.
Dr Cole is British although I know Jo Wyatt is from London but I've played her as Hawke and Imperial Agent but... she sounded so posh! Very upper RP.
Traynor's parents are from London and she was probably born there but raised at Horizon.
According to LOTSB, Jack is from Eden Prime.
Simon Templeman is actually quite versatile with his accent. His uses his Loghain accent for Han'Gerrel and a posh London one for Dr Gavin Archer (which I think is his natural accent).
Kai Leng is a curious one. Troy Baker did a lot of voice over work for anime, so rather than choosing to sound Asianese, he merely uses similar seiyuu-style intonation and projection like the way Kai Leng scream and yell. Honestly, this is what redeem Kai Leng for me... a bit.
Overall, its just what I take from observing the game... and as a non-native speaker or ESL. The accents alone made the franchise itself a lot diverse to me especially the alien characters. But all aliens speaks in their own language (probably except for Mordin) so whatever you hear was filtered by your translator.