Here are some articles on this topic:
Bratati Kahali, Surajit Basak, Tapash Chandra Ghosh. Reinvestigating the codon and amino acid usage of S. cerevisiae genome:
A new insight from protein secondary structure analysis. Biochemical and Biophysical Research Communications 354 (2007) 693–699
Chava Kimchi-Sarfaty, Jung Mi Oh, In-Wha Kim, Zuben E. Sauna, Anna Maria Calcagno, Suresh V. Ambudkar, Michael M. Gottesman. A “Silent” Polymorphism in the MDR1 Gene Changes Substrate Specificity. Science 315:525-8.
A. G. Nackley, S. A. Shabalina, I. E. Tchivileva, K. Satterfield, O. Korchynskyi, S. S. Makarov, W. Maixner, L. Diatchenko. Human Catechol-O-Methyltransferase Haplotypes Modulate Protein Expression by Altering mRNA Secondary Structure. Science 314:1930-3.
Danxin Wang and Wolfgang Sadée. Searching for Polymorphisms That Affect Gene Expression and mRNA Processing: Example ABCB1 (MDR1). The AAPS Journal 2006; 8 (3) E515-E520.
I use the human codon frequency table at KEGG to ascertain allele-specific differences in codons of synonymous SNPs. The above papers then give some idea of effect size of the alleles.
Edit 1 Feb 2011: adding a new paper that has just come to my attention as this seems very neat. The synonymous SNP alters binding of a microRNA such that the protective allele is downregulated by the microRNA and the risk allele does not support binding of that microRNA. See details in this paper by Brest, Hofman, et al. on MIRN196, IRGM expression and Crohn's disease.
Edit 14 Dec 2011: There is a very nice news feature at Nature Medicine on this topic, written by Alla Katsnelson. The theme is "synonymous DNA changes can trigger disease in a number of ways."