You mean like Finnegan ?
(Sorry for self-promoting)

FF Supergrotesk

CORRECTION (edited above):
I'm not looking for shears that are non-perpendicular (implicitly to
the "stroke"), I'm looking for shears that are non-horizontal/vertical.
So perpendicular is even OK - although not required. (You might have
figured all this out already...)

Jürgen, Finnegan is a valid suggestion (with no need to apologize).
Supergrotesk: nope, the shears are generally horizontal/vertical.

A good example of what I'm looking for is H&FJ Whitney.

hhp

ITC Quay Sans

FF Profile and FF Enzo, formerly known here as Zai

So you're looking for a humanist sans? The possibilities are endless.

Actually it doesn't have to be humanist. I'm looking for sans fonts where the terminals are cut at "funny" angles, like Profile. Quay Sans is a great font (takes after papa Syntax), it's über-humanist, and it even has flares, but it doesn't really qualify.

hhp

Try Kabel.

Dwiggins' Metro?

Plantago:

Would Magma by Sumner Stone qualify?

Make Gill Sans the way Gill drew it?

Hrant,
what about GST Polo by Georg Salden then?

(you have to search after >Fonts after style >Sans Serif >GST Polo; i believe the pictures of the English version of the website are not working, so you have to browse through the German version >Fonts nach Stil >Sans Serif >GST Polo)

And as those images are tiny anyway, have a look at this thread for links to useful samples of GST Polo:
http://typophile.com/node/32095

Le Monde Sans?

"What are people’s recommendations for some (non-crazy)
sans fonts with terminals sheared non-horizonally/vertically*?
Flare-serif fonts can apply too."

What 4?

Cheers!

I hope I will also be forgiven for self-promotion, but Anivers came into my mind reading this topic.

What about Jeremy Tankard's Stephenson, Blake & Co. inspired Wayfarer. That has some of the most arbitrary lower case terminals you'll ever see. Check page 3 of this pdf.

I think that Ricardo Santos Lisboa might fit you purposes: http://www.vanarchiv.com/lisboa-introduction.html

Dino

@Margor - Where did you find Plantago? Are you sure that's what it's called, I googled it but came up with nothing.