Sorbitol: Ingesting large amounts of sorbitol can lead to some abdominal pain, gas, and mild to severe diarrhea. Sorbitol ingestion of 20 grams/day (g/d) as sugar-free gum has led to severe diarrhea leading to unintended weight loss of 24 lbs in a 114 lb woman; another patient required hospitalization after habitually consuming 30g/d. Sorbitol can also aggravate irritable bowel syndrome and fructose malabsorption.
If it does bad in large amounts, do I even want to eat a little of it? No, I don't.
After FDA approval, a study published in the Journal of Head and Face Pain reported sucralose as a possible trigger for migraine patients. Another study published in the Journal of Mutation Research linked high doses (2 g per kg; equal to 10,000 packets per day for the 150 lb person in the above example) of sucralose to DNA damage in mice.
Concerns have been raised about the effect of sucralose on the thymus, an organ that is important to the immune system. A report from NICNAS cites two studies on rats, both of which found "a significant decrease in mean thymus weight" at a certain dose. The sucralose dosages which caused the thymus gland effects referenced in the NICNAS report was 3000 mg/kg bw/day for 28 days. For an 80 kg (176 lb) human, this would mean a 28-day intake of 240 grams of sucralose, which is equivalent to more than 20,000 individual Splenda packets/day for approximately one month. The dose required to provoke any immunological response was 750 mg/kg bw/day, or 60 grams of sucralose per day, which is more than 5,000 Splenda packets/day (there are 11.9 mg of sucralose in a 1g retail packet of Splenda). These and other studies were considered by regulators before concluding that sucralose was safe. However, because some ingested sucralose is broken down and absorbed by the body there is concern that chronic consumption may lead to thymus shrinkage or other side-effects.
 Gastrointestinal tract
The bulk of sucralose ingested does not leave the gastrointestinal tract and is directly excreted in the feces while 11-27% of it is absorbed. The amount that is absorbed from the GI tract is largely removed from the blood stream by the kidneys and excreted in the urine with 20-30% of the absorbed sucralose being metabolized. According to one study, sucralose is digestible by a number of microorganisms and is broken down once released into the environment. However, measurements by the Swedish Environmental Research Institute have shown that wastewater treatment has little effect on sucralose, which is present in wastewater effluents at levels of several μg/l. There are no known eco-toxicological effects at such levels, but the Swedish Environmental Protection Agency warns that there may be a continuous increase in levels if the compound is only slowly degraded in nature. Additional research has shown the potential for DNA damage in gastrointestinal organs of laboratory mice.
The basis for concern about the safety of sucralose derives from the class of chemical to which it belongs. The sucralose molecule is an organochloride (or chlorocarbon). Since some organochlorides are known to cause adverse health effects in extremely small concentrations, critics of sucralose feel the extra-high burden of proof is warranted. Although some chlorocarbons are toxic, sucralose is not known to be toxic in small quantities and is extremely insoluble in fat; it can not accumulate in fat like chlorinated hydrocarbons. In addition, sucralose does not break down or dechlorinate.
In contrast to these concerns, many organochlorides occur naturally in food sources such as seaweed.
 Weight gain
Research where rats were given yogurt sweetened with either sugar or saccharin found that the rats given saccharin gained more weight, because they ate more afterwards, presumably due to compensatory effects. It is hypothesized that this effect would apply to all non-nutritive sweeteners, and would also be seen in humans. 
 Allergic reactions
There have been anecdotal reports of "allergic" reactions and other adverse reactions to Splenda. 
High-fructose corn syrup:
Check out the wiki. I eat this stuff, but as little as possible.
All these are from Wikipedia. I'm not making this up.