I've often heard that the artificial sweetener aspartame causes cancer.
Is it true?
If you give more weight to independent scientific research then yes, aspartame may cause cancer in humans. If you prefer industry-funded studies, then the answer is no, aspartame has no adverse health effects for humans.
Independent scientific research has overwhelmingly found health issues with aspartame, in particular that it does cause cancer in rats. A 2005 article from The Guardian references a 1996 review of aspartame research which found that:
...every single industry-funded study found aspartame safe. But 92% of independent studies identified one or more problems with its safety.
The primary independent scientific studies which reported increased tumors in rats originate from the European Ramazzini Foundation of Oncology and Environmental Sciences (ERF), led by Morando Soffritti. They have conducted a number of studies on the carcinogenic potential of aspartame, concluding that aspartame is a potential carcinogen at normal dietary doses:
The results of this carcinogenicity bioassay confirm and reinforce the first experimental demonstration of APM’s multipotential carcinogenicity at a dose level close to the acceptable daily intake for humans. Furthermore, the study demonstrates that when life-span exposure to APM begins during fetal life, its carcinogenic effects are increased.
The primary industry-funded review cited when dismissing safety concerns around aspartame is the 2007 Burdock safety evaluation. As this review was funded by Ajinomoto (the largest manufacturer of aspartame), and conducted by the Burdock Group (an organisation whose commercial focus is on gaining regulatory approval of substances for clients) serious questions have been raised about its validity.
The scientists who led the Burdock safety evaluation had numerous conflict-of-interest issues, including lead scientist Bernadene Magnuson who is a consultant to the aspartame and soft drink industry, and has travelled the world funded by companies like Coca-Cola.
The ERF studies led by Morando Soffritti have also been criticised as flawed, but it is interesting to note that this criticism was led by the Burdock Group. In a letter to Environmental Health Perspectives Soffritti is highly critical of Magnuson and the Burdock Group, drawing attention to their industry funding and accusing them of misleading readers:
Magnuson and Williams’s letter is substantially a repetition of the arguments set forth in a recent article (Magnuson et al. 2007), which was a “safety evaluation” sponsored entirely by Ajinomoto, the manufacturer of aspartame. Their article (Magnuson et al. 2007) and this letter contain numerous erroneous statements about the long-term carcinogenesis studies on aspartame conducted by the European Ramazzini Foundation (ERF).
To support their assertion, Magnuson and Williams mislead readers by stating that “the lung was often the site of lymphoma again in this [second] study.”
The other part of your question is whether aspartame "stays in your body forever". That is not a concern either cited by aspartame critics or mentioned in independent scientific studies, so the answer to that is no, it does not stay in your body forever.
However that particular question is representative of the sorts of claims which can easily obscure legitimate scientific concern over aspartame. By focusing on extreme and baseless claims, and emphasizing a link to the more fringe activist groups (who tend to hold extreme views on fluoridation, vaccination and the like), it becomes that much easier to denigrate opposition to aspartame, and dissuade others from digging into the real science on which concern over aspartame is based.
A good example which illustrate the problems faced by skeptics intent on knowing whether aspartame causes cancer is the Wikipedia article on the aspartame controversy. A number of editors very well-versed in Wikipedia rules have ensured that over the years this particular article maintains an industry point of view. For instance, instead of emphasizing the controversy's basis in independent scientific research, the article gives undue weight to individual activists and a hoax letter:
In spite of this, critics like anti-aspartame activist Betty Martini have promoted undocumented claims that numerous health risks...are associated with the consumption of aspartame... Publicity of this controversy has been spread through an elaborate health scare and "Internet smear campaign" involving hoax e-mails repeating Betty Martini's widely circulated conspiracy theory.
Furthermore, the ERF studies by Soffriti are downplayed and dismissed, without mentioning that the criticisms originate from the Burdock Group:
A review of the literature concurred with these evaluations, finding many possible flaws in the study's design and conclusions, which are also contradicted by other carcinogenicity studies which found no significant danger.
Various attempts at disclosing the industry links of that particular study are eventually removed by editors. A number of concerted efforts at bringing more balance to the article have failed, with a recent attempt resulting in creation of an aspartame page at sourcewatch.
A skeptic wanting to know whether aspartame causes cancer would do well to compare both the Wikipedia version and the Sourcewatch version to get a fuller pictures of the issues around this additive.
According to the National Health Institute, there is no evidence suggesting aspartame causes cancer:
A study of about half a million people, published in 2006, compared people who drank aspartame-containing beverages with those who did not. Results of the study showed that increasing levels of consumption were not associated with any risk of lymphomas, leukemias, or brain cancers in men or women. (Question 2)
Researchers examined the relationship between aspartame intake and 1,888 lymphomas or leukemias and 315 malignant brain cancers among the participants of the NIH-AARP Diet and Health Study from 1995 until 2000. Development of these cancers was not associated with estimated aspartame consumption, refuting a recent animal study with positive findings for lymphomas and leukemias and also contradicting claims regarding brain cancer risk. (Questions 3 and 8)
The study they refer to is Opinion of the Scientific Panel AFC related to a new long-term carcinogenicity study on aspartame by The European Food Safety Authority. It can be found here.
If you're curious about this subject, the whole page on the National Health Institute's site is worth reading. It offers a comprehensive explanation of the finding, avoiding technical terms or linking to their dictionary when the term simply cannot be avoided.
In general with questions like this, you should try to look at all the available evidence and see what conclusions can be drawn from that.
Often you'll be able to find some studies that support one side, and some that support the other, but what does the overall body of research say? Of course it's possible you'll find a similar amount of research supporting either side, in which case the conclusion would be that we don't know yet.
Fortunately, the work has sometimes already been done for you, which is the case with aspartame. In 2007 a review of "the scientific literature on the absorption and metabolism, the current consumption levels worldwide, the toxicology, and recent epidemiological studies on aspartame" was done.
Specifically related to cancer the conclusion was: "The studies provide no evidence to support an association between aspartame and cancer in any tissue." And more in general: "The weight of existing evidence is that aspartame is safe at current levels of consumption as a nonnutritive sweetener."
There's still some open questions from a study newer than those cited in some other answers: Life-Span Exposure to Low Doses of Aspartame Beginning during Prenatal Life Increases Cancer Effects in Rats
This study found statistically significant increases in lymphomas and leukemias in rats fed several times a normal human intake over the course of the rats' lifetimes.
The study also raises concern with the methodology used in earlier studies. Specifically:
The two aforementioned epidemiologic studies (Gallus et al. 2006; Lim et al. 2006) published after our first mega-experiment (Belpoggi et al. 2006; Soffritti et al. 2005, 2006) merit general comment. Both studies consider the eating habits of a large population of males and females 50–70 years of age in the 1990s. Given the time frame of these surveys and the commercialization of aspartame in the 1980s, the subjects’ potential use of the sweetener could not have exceeded 10–15 years. It is difficult to believe that this limited adult period of exposure to APM could confirm or exclude a potential carcinogenic risk. The design of these studies underlines the importance of conducting an epidemiologic study in which exposure to APM is monitored beginning in fetal life, particularly given the use of products containing APM by children and women of child-bearing age.
The Center for Science in the Public Interest, a group which lobbies for truth in labeling, summarizes the issue here, mentioning industry reaction to this study. They note that "It is likely that the new studies found problems that earlier company-sponsored studies did not because the Italian researchers monitored the rats for three years instead of two. The Italian tests remain controversial, with the industry contending that they were flawed in several ways and with the FDA stating its scientists couldn't evaluate the studies because the researchers refused to provide their original data."
So, eh. I don't think there's cause for a panic, but the question doesn't seem completely resolved. It's worth nothing that CSPI doesn't seem to give a blanket "fail" to all artificial sweeteners, currently listing Sucralose (Splenda) as appearing to be safe. Oh, and Neotame as well. In fact, since neotame is 40x sweeter than aspartame, requiring correspondingly lower dosage, that may be the safest bet so far.
Oh, and the idea that aspartame stays in your body forever is nonsense. It breaks down into aspartic acid, phenylalanine and methanol.
The wikipedia page about the "aspartame controversy", especially the safete/health part, has more references than I can easily type here. Check over there for the links included, it seems like a solid piece of work.
A short summary (for references see the original obviously, emph. mine)
Reviews have found no association between aspartame and cancer These reviews have looked at numerous carcinogenicity studies in animals, epidemiologic studies in humans, as well as in vitro genotoxicity studies. These studies have found no significant evidence that aspartame causes cancer in animals, damages the genome, or causes cancer in humans at doses currently used.
Concern about possible carcinogenic properties of aspartame was originally raised and popularized in the mainstream media by John Olney in 1970s and again in 1996 by suggesting that aspartame may be related to brain tumors. Reviews have found that these concerns were flawed, due to reliance on the ecological fallacy and the purported mechanism of causing tumors being unlikely to actually cause cancer.