Another seldom-used construction with "would" is very much conditional, but the mood is indicated more by the subjunctive (I think) of the main verb:

"I would that she were here now."

There's an implied "if" in this case, since it's clear she is not here now. The "would" injects wishfulness, but it's hard for me to see where it contributes to the conditional mood of the sentence, which is established by "were."

"I don't know which is worse: ignorance or apathy. And, frankly, I don't care." - Anonymous