Strong Sad: There needs to be a better word for "weird".
Bad Bad Acting: Many examples, but a particular one from "videography"
"Oh, little Jimmy... is playing lacrosse! Oh, he just scored the winning, ah, lacrosse...point! Oh, his dad was totally there and not at Applebee's. Good shot, Johnn-Jimmy!"
Back from the Dead: The Tandy, the Compy, and the New Paper. They all re-die shortly thereafter.
Bait and Switch: The questions that Strong Bad is asked in the emails have a tendency to be taken in a different direction than the question intended. It is so common, in fact, that on the Homestar Runner Wiki site, it has its own page. The following quote from "1 step ahead", in which Strong Bad is asked by someone named Alex, of Medford, NJ, to glue Strong Sad's hands to his face probably puts it best...
"I'm one step ahead of you, Alex. Though I decided to take it in a bit of a different direction."
...after which Strong Bad glues Strong Sad's hands to his butt instead!
Compy Equals Monitor: The Tandy 400 and the Compy 386 are nothing but monitors connected to keyboards. To demonstrate this, the threats they pose in "Virus" and "Retirement" are nullified when their monitors are somehow damaged beyond (apparent) repair; no word or sight about the keyboards.
Contested Sequel: In-universe, "tape-leg". Homestar doesn't like it because it's a short and rather dull episode, though Strong Bad is compelled to defend it.
Censored for Comedy: In #124, "secret recipes", Strong Bad tells the email senders that if they want to be chefs when they grow up, as they say they do, he offers them a recipe "for cooking The C-H-E-_-T." When The Cheat retaliates against him, Strong Bad tries to cover it up by insisting that the blank letter is actually not an A, but a K: "The Chekt. My family has a great recipe for cooking The Chekt." As seen in an Easter egg, however, The Cheat isn't buying it, as seen in him looking at a cookbook for cooking "a wrestleman".
Couch Gag: Strong Bad almost always starts out with a song or a phrase every e-mail. More often then not containing a pun on e-mail.
Trapped in TV Land: In email #150, "alternate universe", Strong Bad celebrates his big "sesquicentenn-email" by constructing an alternate universe portal and visiting the various alternate realities of the website's body of work, where he meets all of the various duplicates of himself.
Serial Escalation: While many of the first animations were just Strong Bad at his computer, that soon became a mere framing device for some montage or tangent.
Wham Episode: Whenever Strong Bad's computers get destroyed, they tend to be these. The most memorable is "virus".
You Make Me Sic: Strong Bad usually pronounces the misspelled words the way they're spelled, though occasionally he will tab up into the message and edit the errors. Among other things, the character of Homsar was born this way... his name was originally a misspelling of Homestar in an early sbemail.