Fave character(s): Daniel Jackson, Jack O'Neill, Sam Carter, Teal'c, General Hammond, Cameron Mitchell, Janet Fraiser...um, all of them??? Really, in 2003 I would have said DANIEL!!! and Jack (and Sam), but now it's really all of them. Except Vala. I don't love her, but I don't hate her either. (Nothing against CB who I think can really act.)
Fave ship(s): I'm gen. I don't ship on the show. I like the friendships. But that being said...in the fandom, I'll play with show ships.
Ships that I like and I wouldn't be opposed to: Daniel/Sha're, Daniel/Sam, Jack/Sara, Sam/Barrett.
Ships that are fun: Cam/Sam, Teal'c/Vala, Thor/Heimdahl, Sam/Rodney, Sam/Teal'c
Ships that don't bother me either way: Daniel/Janet, Sam/Pete, Jack/Janet, Daniel/Sarah, Cam/Vala, Sam/Martouf.
I also don't mind slash, but I find most of it is worse than some of the worst het.
Ships I don't like: Daniel/Vala. Full stop. Can't stand them. I like it when Vala is as far away from Daniel as possible. Though, at least in S10 they have been more tolerable and I can handle some of the friendship scenes. Strangely enough, my kneejerk reaction to Daniel/Vala (and RDA leaving the show) has allowed my hardcore stance on Sam/Jack to soften. A few years ago, I would have put a hex on Sam/Jack. Now, it doesn't bother me. But don't expect me to start shipping them anytime soon.
Characters I don't like: I pretty much like them all. I don't hate Vala. I just don't like the Daniel/Vala show. I don't hate Jonas, but I don't like how he was always portrayed. My beef is more with the writing than the characters.
Fave episode(s): All time fave is One False Step. But...I love eps for just about every character. Crystal Skull, despite the crappy effects. Fire and Water. The First Ones. Lifeboat. Legacy. But I also enjoy any team feeling eps, whichever those might be. I love TFBTGOG. 1969. Fair Game. The S1 finale/S2 premier. Jolinar's Memories and the other one that goes with it. (I'm a bad fan!) Changling. Avatar. Singularity. Foothold. Cold Lazurus. Zero Hour. Shades of Grey. Fail Safe for Hammond. Avalon for Cameron. I'll stop now...
Reason(s) I started watching: I was bored. I had no show at that time. I wasn't happy with Smallville. X-Files had ended. Firefly had ended. And I was in a job I disliked and longed for my anthropology days of undergraddom. So, I caught the S4 reruns in fall 2003 and then caught the Monday night stacks and the S7 first-half reruns while buying the DVDs ;) I fell for Daniel first because he was doing things I missed. I quickly proceeded to apply to grad school because I kept getting mad he was doing things I wanted to do. Heh heh. I also enjoyed Jack, mainly for the Daniel and Jack friendship and banner. I was secretly shipping Sam/Daniel, but you didn't hear that from me. (And Sam's perosnality is a lot like mine, so I was excited for her.) I ignored Teal'c :( But then I found fandom and got sucked in.
Reason(s) I continued watching: Team. The banter. Mythology. And the entire concept was fascinating to me. You know, until they stopped using the Stargate...;) But really, the cast just had such great chemistry I couldn't stop.
Thing(s) I don't like about this show: I find their ship is forced. If TPTB would just let the characters naturally flow, I don't think ship would be an issue with me. I saw Pete as a plot device. I found a lot of the later Sam/Jack was forced while the early seasons (when they just let the characters be) Sam and Jack had better chemistry. (All the characters did, frankly.) TPTB are now doing the same with Daniel/Vala. When it's not being shoved at us, their scenes are nice. When they hit you over the head with it, it's very annoying. and while I am talking about ships, I hate the Prometheus, the Odyssey and any other fungly space ships they have that takes away from the Stargate. I possibly hate those ships more than Daniel/Vala ;)
So there you go. And yet, I still refuse any character or pairing bashing. I may not like certain pairings or stuff on the show, but it's so much fun knowing people that do :)
ETA: I guess I should say there is some vague talk about seasons 1 through the first half of S10 in the comments, but nothing spoilery to my knowledge.