We report new measurements of branching fractions for 20 UV and blue lines in the spectrum of neutral silicon (Si i) originating in the 3s
23p4s
3Po
1,2,1Po
1, and 3s3p
3
1Do
1,2 upper levels. Transitions studied include both strong, nearly pure LS multiplets as well as very weak spin-forbidden transitions connected to these upper levels. We also report a new branching fraction measurement of the 4P1/2–2Po
1/2,3/2 intercombination lines in the spectrum of singly ionized silicon (Si ii). The weak spin-forbidden lines of Si i and Si ii provide a stringent test on recent theoretical calculations, to which we make comparison. The branching fractions from this study are combined with previously reported radiative lifetimes to yield transition probabilities and log(gf) values for these lines. We apply these new measurements to abundance determinations in five metal-poor stars.