Single fluorophores and single-pair fluorescence resonance energy transfer were studied with a new confocal fluorescence microscope that allows, for the first time, the wavelength and emission time of each detected photon to be simultaneously measured with single molecule sensitivity. In this apparatus, the photons collected from the sample are imaged through a dispersive optical system onto a time and position sensitive photon detector. For each detected photon the detection system records its wavelength, its emission time relative to the excitation pulse, and its absolute emission time. A histogram over many photons can generate a full fluorescence spectrum and correlated decay plot for a single molecule for any time interval. At the single molecule level, this approach makes possible entirely new types of temporal and spectral correlation spectroscopies. This paper presents our initial results on simultaneous time- and wavelength-resolved fluorescence measurements of single rhodamine 6G (R6G), tetramethylrhodarnine (TMR), and Cy3 molecules embedded in thin films of poly(methyl methacrylate) (PMMA), and of single-pair fluorescence resonance energy transfer between two Alexa fluorophores spaced apart by a short polyproline peptide.