Hiccups seem to result mainly from inappropriate stimulation of the vagus nerve, which in its turn stimulates the phrenic nerve that controls the diaphragm. The vagus nerve also controls a wide range of functions in the neck and trunk, including part of your tasting and breathing apparatus, especially near the back of the tongue or the pharynx. It controls the epiglottis, which is crucial in coordinating our breathing and swallowing so that we can eat without choking. Confuse the system, and it produces diaphragmatic heaves cut off by epiglottal clicks: hiccups.

All sorts of things can produce hiccups in that way, such as irritation of areas served by the vagus, or confusion of our eating and breathing rhythms. For instance, belching after eating a bellyful juicy, fibrous fruit can cause a hiccup. Many pungent foods cause some people to hiccup, and so do foods that are hard to swallow, such as mouthfuls of dry bread or floury potatoes. They give the vagus confusing messages concerning the action of the epiglottis in passing food over the top of the trachea while preventing your inhaling it. If food is lubricated, say with butter, or by salivation stimulated by appetising flavours, hiccups are unlikely.

Hooold your breath!

Jon

I do not have any scientific evidence to back this up, but I have been convinced of this for years:

I am an IBS (Irritable Bowel Syndrome) sufferer and I have found that many of the foods that trigger my digestive spasms also trigger hiccups (also a type of spasm).  I am thinking that certain foods are an irritant to the delicate composition of these passages in our body, and it would make sense that some people are more sensitive to these things than others.

Wheat is a food that many people are mildly intolerant to, but often not severely enough to cut it out of their diets. When in its most 'natural' 'unprocessed' form in bread (or perhaps bran flakes) there are still traces of the husks left which I presume are more likely to irritate the body.  The more refined white breads are softer with less 'scratchy' bits and so are less likely to cause any trouble. 

Something I have never investigated is if the remedies for IBS help for hiccups and vice versa - peppermint capsules are good for IBS, perhaps sucking on a mint would help hiccups? 

Lastly, I am not 100% sure there is any connection to this, however it is worth noting that wheat can also cause breathing trouble when inhaling flour or wheat dust - bakers sometimes have a condition known as 'baker's asthma' or 'bakers lung'.  It does support the idea that wheat is generally an irritant to various parts of the body.