Played with in Friendly Hostility: Fox normally has no problem in referring to Collin as his boyfriend, but when Collin shows up while his coworker Derringer is pestering him about becoming buddies, he quickly rushes to loudly introduce him to Derringer as his "BEST FRIEND". Collin just as quickly walks off before he gets mad enough to do something he'll regret.
Issac and Joy in Namir Deiter, though it's only by mutual agreement (and a boatload of issues) that they're not.
Except they've recently been upgraded to Beta/Tertiary couple, after an argument while on a double-date (with different people).
Shadehawk and Crossroad in Antihero for Hire, though with all the UST between them, some feel it's only a matter of time. The most notable example is here:
Hector: Looks like your girlfriend's coming to the party. Shadehawk: Ugh. You are such a depraved monster. Insinuating that she's my girlfriend, I mean.
In The Inexplicable Adventures of Bob!, Bob frequently has to reiterate to his girlfriend Jean that there is nothing between him and the alien Princess Voluptua. Despite the fact that they have kissed. And that Voluptua is now stationed in Earth's solar system. And that she is a Stripperiffically-cladHello, Nurse! of the first order. Because Bob knows that she is in fact, under her disguise, a giant alien bug.
Boris, the robotic spider in Bugs, has shouted more than once that a real spider with a keen interest in him is not his girlfriend.
However, in the short term at least, this turns out to be true. Jack has a crush on Zimmy of all people, and Annie, at the time of making the aforementioned statement, held a hidden grudge against Jack. They're likely in for more teasing of that sort now, though, considering that as far as their classmates are concerned Jack publicly gave Annie a note and some of them saw them amiably chatting then going off on their own for a night. Of course, there's a nonromantic explanation for those, but others don't know that.
Dwayne: That was quite an adventure you guys had. How's Dexter? Patty: Argh! Not you too! Look, we are not dating! We made peace! That's it! Not seeing each other, not dating, not engaged, not getting married, not breeding! "Friends" is pushing the definition! We just aren't fighting anymore!
Several people in Questionable Content refer to Angus as Faye's boyfriend or something similar before they are officially an item, but have admitted their mutual attraction. Faye denies this.
In Ears for Elves, Donny sees Tanna walking arm-in-arm with Rolan. Donny infers that Rolan must be her boyfriend, and finds this disgusting; Tanna protests madly. A while later, Donny tells Tanna that her new boyfriend isn't so bad after all; her reaction is to say that Rolan is not her boyfriend.
In one story arc for Cheer!, Lita forces Alex (who is a girl, yes) to take her out to dinner to a steak house. She also forces Alex to go to the dinner wearing a nice suit. Cue Alex spending most of the evening telling the restaurant staff that she is not Lita's date and not a "sir".
In Footloose, Jenny refers to Keti as Dan's girlfriend - she, Dan, and Iordan insist she isn't in unison, Keti and Dan being genuinely Squicked by the idea, and Iordan having a vested interest in Keti being single.
In Homestuck, Terezi seems to inspire a lot of this. Karkat repeatedly denies having a "thing" with her when numerous other characters notice their bond, and Dave denies dating her when Karkat starts getting jealous.
In Avialae, every relative that sees Gannet and Bailey together assume that they're dating. This is not helped by Gannet's complicated hang-ups with relationships making him fine with doing everything with Bailey but calling their outings together "dates".
Gannet: They think we're dating. This isn't going to help.
Bailey: And we're not?
Manly Guys Doing Manly Things: Variant. Jones has serious commitment issues, and doesn't want to label her relationship with the Commander, even though they do all the normal couple things like spend major holidays together. The Commander, for his part, considers this a small price to pay for being in a stable relationship, and is quick to stop other people when they try to point out flaws in her logic.