How might one go about creating character conflicts that intrigue people? As in, ones that are innovative/original that are not cliched (for example, the love triangle when it was brand new).
The basic block of conflict is "Person or Group A wants something, and Person or Group B wants to stop that." The intrigue and originality are all in the details. Create intriguing characters and give them an original dilemma and you've got interest.
This is a pretty broad question. In high school English we had to tease out conflicts from books. Man v. man, Man v. nature, Man v. God, Man v. machine, and Man v. himself. What we generally found was that there were a lot of conflicts between Man v. man because of a disagreement in opinion on how to deal with one of the other confounders.
So I guess my suggestion, of which I imagine there will be several good suggestions, would be to arrange for a disagreement on an essential variable in the story.
Also, dialogue is generally a good way to encourage opinions in your writing.
How about the character in conflict with himself on whether to give into his depressive urges:
To be, or not to be: that is the question./Whether 'tis nobler in the mind/To suffer the slings and arrows of outrageous fortune,/Or to take arms against a sea of troubles,/And by opposing end them?/To die: to sleep.