The transition to near-field (NF) communications in ultra-massive multiple-input multiple-output (UM-MIMO) systems fundamentally alters the spatial degrees of freedom (DoF) of wireless channels. While the NF DoF of line-of-sight (LoS) transmission channels is well-characterized in the literature, the DoF in NF multipath scenarios remains underexplored. This paper investigates the spatial DoF of NF UM-MIMO channels under practical multipath conditions. A generic DoF metric is derived by modeling multipath propagation and analyzing the resulting eigenvalue distribution based on the Green' s function representation of the channel. The DoF contribution of each path is determined by the product of the effective electrical aperture and the subtended solid angle, and the total DoF is obtained through the effective union of spatially resolvable path contributions. A mapping between the eigenvalue distribution and multipath powers is further established. Numerical simulations and real-world NF channel measurements at 28-30 GHz with 720 array elements are conducted for validation in both LoS multipath and non-LoS scenarios. The results show that multipath propagation can significantly increase the spatial DoF and that the proposed metric accurately predicts the DoF of practical NF channels. The proposed framework provides a practical tool for DoF prediction and supports capacity analysis and spatial multiplexing design in future NF UM-MIMO systems.