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"The Main Attraction"--First single from A Happy Pocket.  I've always been intrigued when bands attempt songs containing tempo changes.  Sometimes it works; sometimes it doesn't.  Thankfully, "The Main Attraction" is an example of the latter.  Quirky/jumpy the first half, smooth and mellow the second.
"Bloodrush"--Third single from I've Seen Everything.  Medium-fast-tempo with brilliant chiming guitar in the chorus. "Don't let my blood rush in vain" is a perfect example of the sort of clever word-play the band has been known for (vain = vein, get it?).
"I've Seen Everything"--Second single from I've Seen Everything.  The official video, like the one for "Obscurity Knocks" and "Only Tongue Can Tell", has been removed from YouTube at the request of Universal Music Group. In lieu of that, here is a fine live rendition. Nice anthemic sort of sound to this one.
"Hayfever"--First single from I've Seen Everything.  Very rich sounding recording, and a classic example of the tendency of the Trashcan Sinatras to create songs that don't adhere to the standard "verse-chorus-bridge" structure of pop music. "I've had women, I've had germs / They're eerie, wild and wailing and seductive in small doses". I'm not sure what that means, but I like it.

This video gained the Trashcans a measure of fame when it was featured on the "True Crime" episode of Beavis and Butthead during the segment where they watch music videos and make juvenile comments. Butthead said he had "a bad feeling about this video", and then stated that the Trashcan Sinatras were "just another bunch of British mama's boys". No such thing as bad publicity, eh?
"Circling the Circumference"--Third single from Cake.  High energy song from the Cake album. No official video was released for this song, but thankfully a fan has placed an audio recording on YouTube (accompanied by the photo of the band shown at left).
"Only Tongue Can Tell"--Second single from Cake.  This is the song that first turned me on to the Trashcan Sinatras and made me go out and buy Cake, their first album (1990). They used to play the official video (alas, no longer available on YouTube) quite a bit on an MTV-knockoff show (the 'original' MTV, that is) that was aired on our local public access channel back in the early '90s. For some reason unknown to me now, it took me a really long time to figure out that they were saying "shin-deep in cement and sand" at the 2:27 mark. I'm not sure what I thought they were saying, but it sounds more clear now.
"Obscurity Knocks"--First singe from Cake.  This obscure video is from an equally obscure American TV show called Onion World with Rich Hall.  This show was on The Comedy Channel (now Comedy Central).  The host, Rich Hall, was best known as a member of the Saturday Night Live cast in the mid '80s.  The Trashcans are shown performing in front of the National Portrait Gallery in Edinburgh during the Edinburgh Festival Fringe, August 1990.
"Obscurity Knocks"--First single from Cake.  The official video for this song was removed from YouTube by Universal Music Group, so this live appearance on a UK variety show will have to suffice. What's with the alien puppet host? Great catchy example of late '80's Brit-pop. Regretfully, the title "Obscurity Knocks" has been unjustly prophetic as success (as defined by wealth and popularity) for the Trashcan Sinatras has not been forthcoming.

Edit--The alien puppet host was called Gilbert the Alien, from a kids' show in the UK called Get Fresh.