Fano resonance results from the coherent interference between a narrow discrete state and a wide continuous spectrum, which is useful for the integrated optical devices. In this paper, Fano resonance in some ultra compact metal-dielectric-metal (MDM) plasmonic waveguides is studied in detail. The structures are composed of a bus waveguide, a stub resonator, a split ring resonator (SRR), or an SRR connected to a tooth resonator (TSRR). The simulation results indicate that the two Fano resonances FR1 and FR2 can be excited, which are sensitive to some of the structural parameters and the refractive index of the dielectric medium in SRR and TSRR. A novel and interesting result is that, for the TSRR, when the rotation angle of its connected tooth cavity is 90° or 45°, the independent tunability of the resonant wavelength of the two Fano resonances can be achieved. In addition, as for the application of refractive index sensor, the sensitivity and the figure of merit (FOM) are both higher. Due to the sharp change of transmission phase shift, larger dispersion will accompany with the Fano resonance. It is shown that the maximum group index can be larger than 14 with optical delay time of about 0.1ps. So the proposed waveguide structures may be suitable for the applications of nanoscale filters, refractive index sensors, and slow-light devices and so on.