Here is a long list of songs that have a certain Smiths vibe to me IMHO:
Sister I'm a Poet
Hairdresser on Fire (but to me, it sounds more like where the Smiths could've gone if they stayed together, not so much like what they managed to release in their 5 years together)
Suedehead
I Don't Mind if You Forget Me
Girl Least Likely To
Piccadilly Palare (to me it has a bit of a Strangeways vibe, so I could see something like this being produced by The Smiths if they'd stayed together like I think with Hairdresser)
You're the One for Me, Fatty
Billy Budd
The More You Ignore Me, the Closer I Get
The Operation (without the drum solo, which I love and could never bear to see removed though, it is standard Smiths to me)
Alma Matters
First of the Gang to Die
In the Future When All's Well
If You Don't Like Me, Don't Look at Me
EDIT: Now I agree with King Leer about A Swallow on My Neck (and Sunny also in my opinion) and Tottenham Tom about I Am Hated for Loving.