There are dozens of hints, references, allusions, and nods in FX's Fargo towards the films of the Coen Brothers. Here is a growing, handy guide that I hope provides a better viewing experience and appreciation for the Coens and Noah Hawley. If you have any further references, suggestions or corrections, feel free to post them in the comment section. Enjoy!  

Episode 1 - The Crocodile's Dilemma
Fargo: On the phone, rehearsing "I don't know what to do"
Fargo: "License and registration, please."
Fargo: The woodchipper at the Lucky Penny
O Brother, Where Art Thou?: Penny is the name of Everrett' wife 
The Big Lebowski: The Dude would be interested in the $2.99 White Russian special


Episode 2 -  The Rooster Prince
Fargo: "Go Bears!"
Fargo: Gustafson parking lot
Fargo: Molly's dinner with a random friend
Fargo: Unguent, the cream Lester and Gaear both put on their wounds
The Big Lebowski: Soiux City (Sarsaparilla)
The Big Lebowski: Similar ransom notes
Hudsucker Proxy: Scraping the name off the window on the door in the office
Raising Arizona: Stavaros and his book American Phoenix point to Phoenix Farms' king Nathan Arizona
A Serious Man: Gus watches his seductive neighbor


Episode 3 - A Muddy Road
Fargo: "funny-lookin' fella"
No Country For Old Men: Mike Zoss
Barton Fink: "I'll leave it up to you, you're the writer"
The Big Lebowski: "Deputy Knutsen" = Bunny's maiden name
Raising Arizona: The accounting firm Malvo drags his first victim from is named McDunnough & Snoats
True Grit: A box in a storage closet in Don Chumph's gym has the name "LeBouef" scrawled on it.


Episode 4 - Eating the Blame 
Raising Arizona/No Country For Old Men - Laying awake in bed at night, staring at the ceiling, making a decision and getting up to do it. 
Fargo: The money hidden in the snow (obvious)
The Big Lebowski: "Uli's" drugstore references Uli Kunkel, the video editor


Episode 5 - The Six Ungraspables
Raising Arizona: "You missed a spot"
Fargo: "I changed my mind, I don't want to park here anymore" conversation with attendant


Episode 6 - Burdian's Ass
NCFOM: "Words and differences"
A Serious Man: The Hebrew riddle
Fargo: The parking garage conversation


Episode 7 -Who Shaves the Barber?
Fargo: The tv is overheard saying the line, "The bark beetle carries the worm to its nest." The same is heard at the end of the film.
Fargo: "Showalter Block" referencing Carl Showalter
NCFOM: Police responding to a load insecurely tied down to a truck
The Man Who Wasn't There: Lester calls a cleanup crew called Reidenschnieder.

 
Episode 8 - The Heap
Fargo: "Diefenbach Realty" is the company on the sign in front of the The Widow Hess' house.
("Riley Diefenbach" was the GM guy calling "Jerry" to explain the missing autos.)  
Fargo: "Are we calm?! Are we calm?!" is similar to "Are we square?! Are we square?!"
Fargo: Marge speech to Gaear/Molly speech to Wrench
NCFOM: Malvo treats his wounds in a similar manner (as well as other characteristics throughout the show)


Episode 9 - A Fox, a Rabbit, and a Cabbage
Fargo: DLR plates
Intolerable Cruelty/A Serious Man: Close-up of teethwork
Intolerable Cruely: (spoiler) Billy Bob playing a doctor
Barton Fink: Finkian hallway
NCFOM: Stephen Root: "Friendo"


Episode 10 - Morton's Fort
Blood Simple: Bullet holes in the wall/door
NCFOM: Carson Wells' name is found on a cassette case in Malvo's suitcase
Fargo: running on a frozen lake
Fargo: "Yeah, you said that already." Carl says that to Jerry in the movie. Lou said that to Lester here.
Fargo: DLR license plate


Sources:
http://popwatch.ew.com/2014/06/17/fargo-film-series-references-season-finale/
http://www.tvguide.com/news/fargo-movie-crossover-noah-hawley-1081378.aspx 
http://letterboxd.com/real_irwin/list/coen-brothers-references-in-the-fargo-tv/detail/
https://tv.yahoo.com/photos/19-coen-brothers-easter-eggs-we-found-in-fx-s-fargo-slideshow/
IMDb.com
My own rotting memory


Also helpful:
Fargo and Blood Simple: http://shinichiro-hamazaki.blogspot.com/2012/01/movie-review-fargo-and-blood-simple.html