TL;DR version : Morrigan, Alistair, Flemeth, Solas, Cole, Anders, Iron Bull, Varric, Leliana (DA:I version), Cullen.
The characters of DA:I are by far my favorites. I'm totally in love with them. Origin was good too. I didn't care much for those of DA:2 except Varric. I'd have to replay DA:2 'cause I don't remember it that well but I do remember having difficulty choosing who I'd romance 'cause I didn't care much for the companions :S Here's my rating :
Origins:
Morrigan : Loved her. Her banter with Alistair was priceless. 10/10. Would recommend.
Alistair : I loved him at first. He was funny. But then he wouldn't answer a f***ing question seriously and QQ about Duncan. EVERY F***ING TIME. Sigh. I hated him then. But then... but then... he toughened up and he was sweet. The way he says "Always" if he sacrifices himself and he romanced you... I... I can't, I'm sorry T_T I need chocolate...
Wynne : Could do without, honestly. I used her a lot in my party 'cause I needed a healer but other than that... meh... 3/10
Sten : He was cool but not that memorable TBH. 6/10
Ohgren : He had his moments. He was fun but he's too stereotypical. Drunk dwarf. Eh... With more nuanced dwarf characters like Varric now, Oghren kinda had his time. 6/10
Shale : Loved her. We need more like her. Crush those pigeons, girl. 8/10
Leliana : I love her hardened personality in DA:I more. In Origins, she sounded too nutty and naive. Still love her to little bits, though. 7/10
Zevran : Eh. He was cool but I don't remember him much. I liked his flirting though XD 6/10
Dragon Age : Awakening.
I'd have to replay it. The only companion I remember is Anders. I liked him a lot then. He was my bro. We'll raise a cat army together, mwahaha.
Dragon Age 2:
I don't remember much so can't give a rating but here goes anyway:
Aveline : I was always walking on egg shells with her. I never knew if I'd offend her or not. Pass..
Anders : My little Anders. LET ME HUG YOU!!
Fenris : I SO wanted to like him but he was always angry with me, dammit. I remember really liking his voice actor though.
Isabela : She had her moments. Had a good laugh with her.
Merrill : She annoyed me. Period.
Sebastian : No idea. Didn't buy the DLC.
Varric : Best bro forever!!! 10/10. I'd want him in every game.
Dragon Age : Inquisition
Cassandra : Not my favorite but liked her enough. The "Good book?" scene is one of my favorite in the entire game. GASP. Nothing should happen to her. Oh, Cas, my little romantic you. 7/10.
Solas : On my first playthrough, he was my bro!! Loved him to bits. I happened to agree a lot personally with his views. After seeing the epilogue, I HAD to play a Dalish and romance him. Even though he broke my heart (which I'm still recovering from. Yes, I know, it's a game, they're not real but.... BUT!!! T_T) I love him even more. My little fade-tongue idiot.
I love his voice actor. I would have loved if he had more stories about the fade to tell. I could listen to him talk forever. His voice actor couldn't have done a better job. 10000/10. Can't live without. Can't wait to see him again, for better or for worst.
Varric : Glad to have you back, bro! Wouldn't be the same without you! Sorry about killing Hawke though... erm... 10/10 Pick me up for a game of Wicked Grace anytime.
Sera : I loved her when she was introduced. Her voice actress did a GREAT job with her. Obey me, arrow in my face. However, I began to like her a little less when she started denying everything she saw and heard. When she laughed at my Lavellan for removing the Vallaslin, I kinda began to hate her. That was a douche move, Sera. But she baked me cookies afterwards so we're slowly recovering. 7/10
Vivienne : Hate her. She has NO redeeming qualities for me. She's an utter ******, shallow as you can be and unless you do EVERYTHING she'd approve of, you'll never get in her good graces. Well, ****** on that, my dear. I don't even recruit her anymore. I'd bring f**ing Joffrey Baratheon in my party before I'd bring her. 0/10.
Cole : He's my BABY. He's just so adorable. I like the way he talks. I'll never NOT recruit him. I brought him everywhere. It comes off. I didn't know it came off. 100/10 I want him in my party forever.
Iron Bull : He made me laugh all the time and he's a very decent guy. Very down to earth. LOVE HIM. I'll have to romance him at some point. 9/10.
Blackwall : I romanced him on my first playthrough 'cause at first he seemed like a decent, solid man. I quickly regretted my choice with all his QQ about how "oh no, we can't. we musn't". Solas had similar lines but at least he'd still make out with you >.> and grab your butt. I broke up with him while judging him and sent him to the Grey Wardens. Everytime I talked to him he sounded like he was disappointed in me or was scolding me like when you pick up a grey warden item and he's not in the party. Way too dark and broody. Well, screw you, Rainier. 2/10
Dorian : He was my best pal!! I loved the fact you could still flirt with him even after he admits he's gay XD His banter is hilarious. Oh, Dorian, NEVER change. 9/10
Cullen : I ADORE HIM. His romance is so squee worthy. I'm actually GRATEFUL that Cullen exists. After romancing Blackwall and Solas, it was nice to have someone solid at your side. I know he's already been in all 3 games so far but I wouldn't mind seeing more of him in future games. I loved how quickly he reacted during the attack on Haven. Good on you, mate. The chess scene was really cool and heart warming. It gave life to the game for me. 9/10
Josephine : Meh. I don't know. She's fine I guess. Did her job well. Only time I ever liked her was during the Wicked Grace scene. Other than that, I didn't care much for her. No particular reason. Just not memorable. 5/10
Leliana : I like her Inquisition so much better!!! She's darker, in charge and knows who she is and what has to be done. THAT SCENE IN REDCLIFF. I wished she had had more arrows... <- reason #1 to side with the mages instead of the templars. Just for that scene. 10/10
Others :
Flemeth : LOVED Flemeth from the start. One line that stuck with me ever since I heard it : [Answer : I'm not sure what to believe] A statement that possesses more wisdom than it implies. Flemeth always had the most well thought replies. When she told my Lavellan in Inquisition "You do the People proud and have come far", I wanted to hug her like she was my mom. : DIES: Throughout the game, people keep telling you how awesome you are and you're the only one they'd trust to be the Inquisitor and blah blah Herald of Andraste blah but for me only Flemeth's compliment seemed sincere.
Briala : Haven't read the book but I really liked her in Inquisition. Kinda wished they explored her more. Oh well.
Bianca : Her banter with Varric was priceless XD
Tallis : FELICIA DAY
<- My personal Goddess
Duncan : Too bad he died so early in the serie. I would have liked to see him more 
The Chargers : I don't think I'll ever be able to choose to sacrifice them. It's a BOW.
Mother Gisele : She's pretty decent for a Chantry lady. I think of her as Flemeth's equal in some ways. Very good advice and wisdom in her own way.