Recently I went to write "Seems a plague" as in "The self doubt that seems a plague in todays youth." Is this grammatically correct?
It depends what you are trying to say. Seems, appears, impression etc. are not definite. Whereas, 'Self doubt is a plague in todays youth', has no doubt.
I don't think you can have a plague "in" something. Maybe one way of writing what you wanted to was: There seems to be a plague upon today's youth. That plague is self doubt. Is that what you were after?
As abe indicates, the bit in the sentence that gave me pause was the in not the seems. I suspect in here is not technically incorrect but certainly that formulation is rather odd and perhaps ugly.
in your example, 'seems' needs to have 'to be' after it to make any sense... however that whole sentence isn't a sentence, anyway... it's a fragment that doesn't work on its own, but could, depending on what came before it... plus: 'todays' is missing an apostrophe 'in' makes little sense, as noted above
I would say YES if it's being used in informal conversation. Otherwise, "it seems to be a plague" would probably be more appropriate.
Maia's suggestion of "to be" or using "like" ("seems to be a plague", "seems like a plague"). I also agree with folks concerning "upon" or "on" instead of "in". I don't know about the actual grammatical correctness of either in your original sentence, but they both make me pause and reread, so probably don't serve your interests as a writer very well.
Oops! Look at me mucking up my example sentence. It's not the full sentence, anyway, just the snippet that I was referring to. Thank you for the advice, I do tend to use it that way when I'm speaking among friends, but generally not in my non-informal writing.