Deep sequencing of transcriptomes has become an indispensable tool for biology, enabling expression levels for thousands of genes to be compared across multiple samples. Since transcript counts scale with sequencing depth, counts from different samples must be normalized to a common scale prior to comparison. We analyzed fifteen existing and novel algorithms for normalizing transcript counts, and evaluated the effectiveness of the resulting normalizations. For this purpose we defined two novel and mutually independent metrics: (1) the number of “uniform” genes (genes whose normalized expression levels have a sufficiently low coefficient of variation), and (2) low Spearman correlation between normalized expression profiles of gene pairs. We also define four novel algorithms, one of which explicitly maximizes the number of uniform genes, and compared the performance of all fifteen algorithms. The two most commonly used methods (scaling to a fixed total value, or equalizing the expression of certain ‘housekeeping’ genes) yielded particularly poor results, surpassed even by normalization based on randomly selected gene sets. Conversely, seven of the algorithms approached what appears to be optimal normalization. Three of these algorithms rely on the identification of “ubiquitous” genes: genes expressed in all the samples studied, but never at very high or very low levels. We demonstrate that these include a “core” of genes expressed in many tissues in a mutually consistent pattern, which is suitable for use as an internal normalization guide. The new methods yield robustly normalized expression values, which is a prerequisite for the identification of differentially expressed and tissue-specific genes as potential biomarkers.