In general, dominant alleles do not silence the expression of recessive alleles. How exactly an allele functions as dominant or recessive depends on the exact biochemical function of the genes involved. Many dominant alleles code for a protein that causes a specific function and recessive alleles are loss-of-function mutatants. As long as you have one copy of the correctly functioning allele, the gene is still able to perform its function correctly, so the defect shows up only when both alleles of the gene are not functioning correctly.
Recessive alleles sometimes contain mutations that prevent expression of the protein. In these cases, the gene will be expressed from the dominant allele but not the recessive allele. This is not always the case, however. For example, in those heterozygous for cystic fibrosis, the CFTR protein is expressed from both the dominant non-disease allele and the recessive disease allele, but the protein produced from the disease allele does not fold properly and gets degraded. Even though ~ half of the CFTR protein gets degraded, the CFTR produced from the non-disease allele is sufficient to ensure correct function, so those heterozygous for the cystic fibrosis allele do not develop the condition.
Incomplete dominance can be tricky. The classic example is the color of snapdragon flowers with RR giving red flowers, Rr giving pink flowers, and rr giving white flowers. Here, I suspect the R allele encodes for the protein that produces the red pigment and the r allele contains a mutation that prevents correct expression of the red pigment-producing protein. In this case, only the R allele is correctly expressed. However, there are probably cases of incomplete dominance where both alleles are expressed.
Here's probably a good resources to read for more information:
http://en.wikipedia.org/wiki/Haploinsufficiency
jedishrfu's post refers to a more advanced topic in genetics called
imprinting, which occurs ins a some specialized cases.