Unimolecular and bimolecular hybridization probes for the detection of nucleic acid target sequences comprise a target complement sequence, an affinity pair holding the probe in a closed conformation in the absence of target sequence, and either a label pair that interacts when the probe is in the closed conformation or, for certain unimolecular probes, a non-interactive label. Hybridization of the target and target complement sequences shifts the probe to an open conformation. The shift is detectable due to reduced interaction of the label pair or by detecting a signal from a non-interactive label. Certain unimolecular probes can discriminate between target and non-target sequences differing by as little as one nucleotide. Also, universal stems and kits useful for constructing said probes. Also, assays utilizing said probes and kits for performing such assays.