TL/DR: There is evidence both ways — it's controversial.
Recent review studies
According to Domingo et. al. (2011), who did an overview of studies into this question, the number of references concerning human and animal toxicological/health risks studies on GM foods/plants was very limited.
Domingo, J. L. & Giné Bordonaba, J. Environ. Int. 37, 734–742 (2011). Weblink.
The article is behind a paywall, but the abstract summarises:
An equilibrium in the number research groups suggesting, on the basis of their studies, that a number of varieties of GM products (mainly maize and soybeans) are as safe and nutritious as the respective conventional non-GM plant, and those raising still serious concerns, was currently observed. Nevertheless, it should be noted that most of these studies have been conducted by biotechnology companies responsible of commercializing these GM plants
This review was from 2011.
An example of a peer-reviewed study concluding harm
More recently, Séralini et. al (2012) conclude that a particular kind of genetically modified food is harmful to rats, but only on timescales similar to the rats lifetime, which would suggest that effects in humans may only become visible on a timescale of decades.
Séralini, G.-E. et al. Food Chem. Toxicol. http://dx.doi.org/10.1016/j.fct.2012.08.005 (2012). Long term toxicity of a Roundup herbicide and a Roundup-tolerant genetically modified maize
This article has sparked considerable debate, as can be seen from the responses and the responses to responses in the sidebar of the article linked above. An article in Nature from 25 September 2012 covers the debate:
Nature 489, 484 (27 September 2012) doi: http://dx.doi.org/10.1038/489484a
Citing from the Nature article:
The study, published in the peer-reviewed journal Food and Chemical Toxicology, looked for adverse health effects in rats fed NK603 maize (corn), developed by biotech company Monsanto to resist the herbicide glyphosate and approved for animal and human consumption in the European Union, United States and other countries. It reported that the rats developed higher levels of cancers, had larger cancerous tumours and died earlier than controls. The researchers have not conclusively identified a mechanism for the effect.
Many scientists, however, have already questioned the study’s methodology and findings. They assert that the data presented in the paper do not readily allow the claims to be independently assessed, and they question the study’s experimental design and its statistical analysis of any differences between the treated groups and controls. Other scientists point out that the Sprague-Dawley strain of rats used in the experiments has been shown to be susceptible to developing tumours spontaneously, particularly as they grow older, making it difficult to interpret the results. Monsanto itself said that the study “does not meet minimum acceptable standards for this type of scientific research”.
Resolution of the debate over the safety of GM foods can come only from rigorous science clarifying the issues, Kearns [head of food safety, nanosafety and chemical accidents for the Organisation for Economic Co-operation and Development in Paris] adds.
I can recommend reading the Nature article.
In June 2012, Michael Antoniou (PhD in molecular genetics), Claire Robinson (director of Earth Open Source) and John Fagan (PhD in biochemistry) published the report GMO Myths and Truths, where GMO is understood as genetically engineered crops. This 123-page document contains an overview of scientific (mostly peer-reviewed) literature critically examining claims made (mostly by industry) about safety and efficacy. This is not an objective report, but rather a collection of scientific results that show that there are risks, either to humans or otherwise. Quoting from the executive summary:
However, a large and growing body of scientific and other authoritative evidence shows that these
claims are not true. On the contrary, evidence presented in this report indicates that GM crops:
Can be toxic, allergenic or less nutritious than their natural counterparts
Based on the evidence presented in this report, there is no need to take risks with GM crops when
effective, readily available, and sustainable solutions to the problems that GM technology is claimed to
address already exist. Conventional plant breeding, in some cases helped by safe modern technologies
like gene mapping and marker assisted selection, continues to outperform GM in producing high-yield,
drought-tolerant, and pest- and disease-resistant crops that can meet our present and future food
Surely, the scientific debate continues.