Assassin's Apprentice

It's a no brainier to read her other books set in the same universe: Live Ship Traders trilogy (set in the same world, but with different characters), and Tawny Man trilogy (direct sequel to the Assassin trilogy).  Her newest trilogy Fitz and the Fool, taking place years after the Tawny Man trilogy, with book one released late 2014 (and to awesome reviews). Also try her Soldier's Son Trilogy; it has a feel that's similar to (yet different from) her Farseer series (less well received by fans and reviewers though). 

Guy Gaverial Kay's Tigana. This book is packed with emotion. If you like the emotional intensity and pathos of Hobb, you will love Tigana.

In terms of style of prose and storytelling, the closest you'll find to Hobb is in my opinion Lyn Flewing. You can start off with her Nightrunner series, about a thief type character OR you can read her best work, The Tamir Triad, which is a magnificent trilogy -- completely character driven, horrific, dark and disturbing. And it's a series you can't put down. It brings to mind the Farseer trilogy when you read it -- not in plot, but in the way the story is told, the horrific things that happen, the wonderful writing, and the intense focus on the characters that drive the story forward rather than pure action.

The Name of the Wind is a good read if you like the compelling characterization of the protagonist. 

Also read Blood Song by Anthony Ryan's got a first person narration like the Farseer, a coming of age story, and strong characterization. If you like The Name of the Wind and Farseer, I'd be shocked if you didn't love Blood Song.

Also, if you are bedazzled with the Assassin mythos of her world, try reading Brent Weeks The Way of Shadows. Weeks is a new force on the fantasy scene with his Night Angel trilogy. With all the action, magic, and adventure, Weeks is like the John Woo of the fantasy scene, but with a grittier edge. I can't say the books are really "deep" by any means, but if you are looking for a series that's a bit dark with over the top action, magic, romance, and a teen hero full of angst, read it.

Prince of Thorns is another series that features an assassin protagonist. This is some dark anti-hero fantasy that's written in first person (like Farseer). However, the protagonist does some pretty horrific things to achieve his goals -- unlike Fritz, who for most of the story, acts like everyone's favorite doormat. If you want to read a much darker, amoral and selfish version of Fritz, one who's not afraid to seize what's rightfully his and damn anyone or anything that stands in his way, this might be one to take a good look at. It's some of the best fantasy that has come out recently, and is a must read if you like your fantasy gray and gritty; if not, skip this recommendation.

Try reading The Hundred Thousand Kingdoms by N.K Jemisin. The protagonist is female and it's written in first person with a good amount of emotional weight. There are a few similarities -- both protagonists were related to powerful families and were, for the most part, abandoned by their family line. Both are stories about a rise from obscurity to importance in a place where royal intrigue and power struggles are part of the norm.

For a non-fantasy book that will have you emotionally involved in the protagonist, you might want to give Ender's Game a read. Being science fiction, there is nothing similar about the plot itself, but it's also a detailed look at the struggle of a young boy who doesn't have a lot of options and who must struggle to survive in an unfriendly world where the odds are stacked against him. A superlative science fiction novel all round.

For an emotionally weighted story about a down-and-out soldier who becomes involved with politics (and saving a young woman who's part of that court), give Lois McMaster Bujold's Curse of Chalion a read. It was a Hugo nominee. The sequel, Paladin of Souls, won a Hugo. Both books are written in a style similar to Hobb's Farseer and the characters are complex and deep -- especially the protagonist. The relationships between characters is also very well done. Well recommended for anyone who likes character-driver fantasy tales.

For less "epic" fantasy recommendations, try Rai-Kirah by Caron Berg which is a very well written character-driven fantasy. 

Give the Sevenwaters books by Juliet Marillier a good look. It has some deep characterization of the protagonists and a very strong romantic bent to it (if you liked Hobb's Liveship Traders, then absolutely read this one).

 For another character-driven (kinky) romantic fantasy series, you may also give the Kushiel books by Jaqueline Carey a read.

For an epic military fantasy with some serious characterization, I recommend John Marco's Tyrants and Kings series. The series is about a man who abandons his kingdom and betrays an empire and turns traitor for the love of a woman who's an enemy of his country. I felt Fitz Chivalry and Marco's protagonist, Richard, had some similarities. Both books are heavy on characterization, politics, and angst.

And for a fantastic low-fantasy series with some of the best characterization I've seen, read Jennifer Fallon's Second Sons trilogy.

For some of the best fantasy about a badass assassin (not the bitch version of an Assassin that Fitz is), you must read the Heroes Die series by Matthew Stover. Some of the best stuff written in the Fantasy genre, and there are no other books as viscerally action-packed. Caine, the hero, takes violence to a whole new universe. It's not all just violence though. The Caine novels are sharply written and the plot is strong as steel.

For a book with a young, scrappy female protagonist/assassin, you can't do better than Maria V. Snyder's Poison Study.

The Crown Conspiracy by Michael J. Sullivan tells a light fantasy adventure tale about a thief falsely accused of being an assassin. It's a much lighter read and the characterization is not as well done, but worth a read if you want an adventure romp involving a pair of irascible rogues.

You may also like Mistborn by Sanderson -- the main character in the first book is sort of like a badass magical assassin/thief/terrorist who kicks ass.

And finally, read any The Book of Jhereg by Steven Brust. They are a different, but still pretty straightforward pulp fantasy fiction series: there's a ton of humor with a strong anti-hero. Don't expect the level of complexity of some of the other recommendations, but the series is a full adventure to follow.

The Bone Doll's Twin. Dark magic, mystery, coming of age, a kingdom in turmoil and gender issues? Sounds like a hit, and it is. The Bone Doll's Twin is the first book of the Tamir Triad (which is completed) and one of the most underrated fantasy books out there. Strong, compelling characters, a strong plot, and superbly written. The voice and tone of the author are somewhat similar to that of Hobb.

Have a look at Sword of Shadows by J.V. Jones. This is more of a modern sword and sorcery than Farseer, but the characterization is outstanding and both stories involve a coming of age with a young man (eventually) cast out of his home into the greater world and forced to find his place in the world. Both feature male protagonists with unique magical powers. Both characters suffer greatly. The authors of both books are female as well. The only problem is, well, Jones has NOT yet finished the series we are still waiting (it's been almost 5 years since the last book).