Terrence of KateModern is an unusual case. When he reinvents himself as bespectacled, cardigan-sporting religious nerd Terry, he is recognised almost immediately by the other characters. However, it somehow doesn't occur to them that quiet, harmless Terry might be the murderer. He later plays this trope straight as the straight-jacketed Patient # 12.
In Englishman, Englishman's Battle Butler (known only as Butler) also moonlights as a supervillain named The Butler. A deconstructed example in that it appears to play this trope straight (E'man never connects the two) but Butler never actually bothers with a disguise, rendering it PoMo.
One College Humor video that is a Take That to British Petroleum's response to the 2010 Gulf oil spill. Tony Hayward and other executives in BP's London offices announce to us after showing a video from an actual focus group that cleaning up the spill is difficult, so they're changing their name to Baby Otter Smiles & Co. Then Hayward and another employee Sally Harris (both of whom are wearing false mustaches) go to the house of Sarah Schneider (one of the focus group members). Sarah sees through their cover, says "You guys are monsters," and shuts the door on them.
Yu-Gi-Oh! The Abridged Series: Despite hiding his face and body well, Bandit Keith still frequently uses his catchphrase (...in America!) while disguised, and still uses the same deck (but to be fair, seeing as how he was a regional champion, it could have easily been Netdecked to hell and back).
Averted in the anime, as Yugi's smart enough to figure out who it is from the deck theme. However, it's played straight a few arcs later when Yugi's grandfather enters the KC Grand Prix and duels Joey...the only one who didn't see through his disguise.
Bubs' alter ego, The Thnikkaman, consists of him wearing sunshades and a piece of paper reading "TH" taped to his chest. And on a couple occasions he momentarily removes the shades. Only Homestar, The Ditz, ever sees through the disguise.
As part of the annual Strong Sad Lookalike Contest, the Cheat dresses up as Strong Sad's left foot by sitting in a paper bag that had an elephant foot crudely drawn on it. Nobody else's costume is particularly convincing either (except for Homsar, who was disqualified because Coach Z thought he actually was Strong Sad), but the Cheat has somehow won the contest three years in a row this way.
Also applies to Strong Bad's attempt to use a stunt double in the Dangeresque trilogy. The stunt double in question is clearly Strong Sad, and the terrible editing does not help.
In Doctor Horrible's Sing-Along Blog, the titular character is not recognized by Penny, even though neither his "costume" or his "normal" clothes covers his face (he wears goggles, but only on his forehead until the last scene).
Possibly justified in that Penny may or may not have heard of Dr. Horrible: she never mentions him; he's not a big time supervillain (yet), and the first time she sees him, she is under a lot of stress, but still ends up recognizing him.
Most people miss Billy in the back of the soup kitchen as he glowers at Captain Hammer and pours the soup back into the pot instead of into the bowl. The irony of it is his idea of disguise is wearing a fake mustache and an apron and not wearing his hoodie.
Paper-Thin Disguise is also subverted, as when Captain Hammer meets Billy, he instantly recognises him as Dr Horrible.
Linkara: Oh wait! I know this one! You're That Chick With The Goggles! Dr. Insano: But- but- I'm not freaking black! Linkara: But you are a woman, eh?
Subverted in Kickassia, when several people recognize Spoony as "that doctor guy", despite his frantic efforts to pretend he's not Insano.
Another Kickassia example. During the invasion the President of Molossia Kevin Baugh disguises himself as Baron Fritz von Baugh, Minister of Making Things Orderly. Although it is obviously him in disguise The Nostalgia Critic decides to go along with it and lets him stay. As it turned out doing this was a huge mistake on the Critic's part as it allowed Baugh the chance to plant a Apple of Discord within his already grumbling troops further sabotaging the future of Kickassia.
Ultra Fast Pony: in "Utter Lunacy", Spike the dragon successfully disguises himself by wearing a dragon costume (one which doesn't even cover his face) and speaking with a different accent. The only time he comes close to getting caught is when he briefly switches back to his normal accent.
In The Time... Guys episode with Timmy's Spanish teacher, Seńor Tigre instantly realises that Dr. Chronos is not Timmy's father when Doc takes his multiple neckties off.
This is used for fun when Lindsey Stirlingdresses up as her own #1 fan Phelba — the only disguise is that Phelba has thick black glasses. A few people realize that Phelba and Lindsey look rather too similar, but since not enough people know them it generally works.
On certain Sparks Nevada segments of the Thrilling Adventure Hour we encounter an alien shapeshifter. Although the alien is always voiced by Paul F. Tompkins and speaks in the same goofy, high pitched tone regardless of who he's impersonating, the other characters are always completely fooled by the impersonation.
Justified, perhaps, in that this is an audio podcast, and it's possible that in-universe, the shapeshifter's actual physical disguise is impeccable. Still, you'd think somebody would ask him why he's talking like that once in a while.
In We Are All Pokémon Trainers, Lenore (Fool's Hydreigon) and Ammy (Umbra's Volcarona) use these to get their own Trainer's Licenses - they wore fake moustaches and trenchcoats. Lenore's case is more notable, because while Ammy was wearing a Pokémon-to-Human armband, Lenore wore the disguise as a Hydreigon.