Vintage Rolling Stones button is an example of cool band swag.
You'd probably have a tough time out-weirding some of the band merch that's out there today, like the Wavves weed grinder, the strange and sometimes gory Ween coloring book, or Pharrell William's curious alcoholic chick-drink called Qream. I guess it isn't always weird stuff that sells, but there is a good lesson in that, and that would be to make phallic shaped objects know thy fan.
Richard Dean Anderson is probably about the only guy in this world who could brag about a "good mullet", but in time it seems like most bands develop their own trademark hairstyles, makeup designs and fashion that their fans adopt and emulate, from Bryan Adams' plain white shirt to Avril Lavigne's faux-punk tie-on-tank look to Lady Gaga's simultaneously sexy and grotesque freak show Halloween antics.
This is where understanding your fan is important, because how they identify your band and your music might be different from how you see it. You guys might think it's the backwards ball caps that your fans remember, meanwhile it could just as easily be those bad, sweaty, ugly brown-and-orange shorts the drummer's been wearing this whole time (hint: try to create positive visual triggers, whenever possible).
People like to have a sense of belonging, you know? The sooner you can give them that feeling of being a part of something - a tribal movement - the better. Music isn't just something people listen to. It's something they experience together.
So take what you find and transmute it over into the button world. What are some prominent standalone elements that really "stick" out to your fans (again, no ugly shorts) and consider how you could depict those on a simple pinback button. This process is really no different than creating a recognizable brand, linking images, objects and words together in a manner that people can immediately identify as being you.
Here are some lessons you can take from other bands and the atrocities merch they've created.
Play on Words
As a merch item, heavy metal outfit Mastodon has a bright red pair of shorts that reads "Asstodon" on the back. It would take a brave soul to wear them, but tacky or not, they're definitely memorable.
So, if you can find a clever play on words (hint: it has to be clever), in whatever capacity, you could integrate it into your button design.
For example, if your band name is Brick Wall, you could create a button that reads, "Have a ball with the boys from Brick Wall". It rhymes, it's catchy, and it's easy to remember. If the catchphrase somehow represents your musical stylings, all the better.
Use Memorable Lyrics
Sometimes designing a great button is simply a matter of taking an awesome, unforgettable lyric from one of your popular songs and printing it in big bold yellow letters (note: they don't have to be bold or yellow). It might sound cheesy, but it has worked before, and it will work again!
It's like the Morrissey pillowcase that reads, "Last night I dreamt that somebody loved me", which refers to the Smiths song of the same name. If people buy pillowcases with lyrics on them, you can rest assured they'll buy buttons with lyrics on them too.
Use Congruent Imagery

This comes back to the question, "how do people remember you?" R&B and soul artist Remy Shand usually wore some kind of beanie or hat. Kiss is famous for their comic-book personas and makeup. Devo is remembered for their weird red hats and shiny, matching space-suits. Seems like a lot of artists wear weird stuff on their heads.
It's like how people almost always associate death with metal music. For better or worse, the skull-and-rotting-flesh imagery has stuck for the genre. If you play metal, you could create some variation on that. Death sells, right?
So, in short, pinpoint a fairly obvious visual trait of the band, deliberate or unintentional, exaggerate it, and exploit it put it to good use.
Make it Novel
From "Weird Al" trading cards to Metallica skateboards, appealing to the novel sense can be one way to make your buttons stand out. Even if it serves no practical purpose (and this can be the downfall of novel merch), creating fun, collectible items is a great way to make memorable swag.
One way to take advantage of this idea is to create a series of buttons that spell out your band's name one letter at a time. You could have separate buttons with each band member's face on it. You could have a sequence of buttons where each one represents a "puzzle piece" that your fans have to piece together.
You might also be able to sell more buttons as a set when they are collectible, novelty items.
Make it Bizarre
We've already pointed out some of the weird merch items out there, but that was just the tip of the iceberg. From Slayer "holiday" sweaters, Weezer snuggies, AC/DC grill mitts, all the way over to Tenacious D cum rags and Rammstein dildo kits, there really isn't any shortage of strange and unusual swag in earthly existence. If someone thought of it, it's probably been done (although at times it goes over like a led zeppelin).
A note of caution about bizarre merch: it's pretty much a roll of the dice whether or not it's going to catch on. It doesn't always work out to your advantage, but like the KISS kasket, there's almost always a niche demographic for anything.
It's like how there's people who still listen to cassette tapes. What? Vinyl records are also making resurgence? Dear god...
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