OOhhh good question!!!!
I bet Leftwood/Rick will have a few to reccomend-
I wonder if the MN Conifer Society has a web site to look and learn from....
Thanks for the post!
Julie

Well, popular unusual is a bit of an oxymoron, but we know what you mean. No clue here if you are looking for dwarf or regular size trees, but here are a few of the more common suggestions:

Arborvitae(Thuja occidentalis 'Degroot Spire,' 'Rheingold,' 'Sunkist,' 'Yellow Ribbon,' 'Tiny Tim,' 'Hetz Midget,' 'Spiralis')
Threadleaf False Cypress(Chamaecyparis pisifera 'Filifera Nana,' 'Filifera Aurea,' 'Filifera Aurea Nana,' 'Lemon Thread,' 'Vintage Gold,' 'Sungold')
Norway Spruce (Picea abies 'Nidiformis,' 'Parsonii,' 'Mucronata,' 'Elegans,' 'Little Gem,' 'Acrocona,' 'Pendula')
Colorado Spruce (Picea pungens 'Globosa,' 'Pendula')
Hemlock (Tsuga canadensis 'Pendula,' 'Jeddeloh,' 'Hussii,' 'Cortorta,' 'Nana Gracilis,' 'Jervis')
White Pine (Pinus strobus 'Blue Shag,' 'Nana,' 'Pendula,' 'Wintergold')

No Minnesota Confer Society, just the national:
conifersociety.org I am a member, and we had the regional meeting in Minneapolis last year.