Like the typical American, I grew up eating wheat and lots of it. And I really enjoy the taste. Furthermore, whole wheat has a powerful anti-cancer compound (phytic acid) and the germ is packed with vitamins and minerals. In spite of all these good things, I try not to touch the stuff. As I've already mentioned, I don't trust what modern agriculture has done to the wheat genome in the last fifty years, something that I discuss in My Review of Wheat Belly. But the main reasons that I avoid are what it does to a) blood sugar / insulin and b) lipids.
On this page I am mostly going to talk about the latter and show you how wheat can negatively impact lipids. This is one of the big reasons someone going vegetarian, vegan or low fat can get themselves in trouble: some men will substitute a bunch of wheat for the old way of eating. As we'll show below, this is likely to get them into trouble and we show wheat is a decided underperformer:
1. CON: Increase Cholesterol in Adults (Men and Women). This study took adults in the top half of cholesterol values and gave them either oat bran or wheat bran while on an American Heart Association Diet. As I document in my page on How to Lower Your LDL Naturally, the oat bran lowered both LDL and total cholesterol. Wheat cereal, on the other hand, raised both total cholesterol and LDL by 3.3% and 4.0%, respectively. 
2. CON: Neutral Cholesterol in Men with High Cholesterol. Those with high cholesterol tend to experience bigger drops with medical and nutritional interventions than those whose cholesterol is already on the low side. Basically, "the bigger they are, the harder they fall." Again, oat bran was shown in those with high cholesterol to powerfully lower cholesterol and LDL by 12+%! 
Now guess how much wheat lowered cholesterol in high cholesterol patients? Zippo! That's right - wheat could not even lower cholesterol in high cholesterol patients. Rememember: plant foods are generally good at lowering cholesterol (and blood pressure). Unfortunately, wheat appears to be an exception to the rule. This means that wheat likely has some pro-cholesterol properties that overcome the fiber, nutrients and other phytochemcials that would normally improve lipids.
3. CON: Neutral Cholesterol in Overweight Senior Men. As in the above oat bran study, barley significantly lowered total cholesterol and LDL, where as wheat did nothing.  Again, that's nothing to brag about in the world of plants.
4. CON: Increase of Particle Count, Small Particle LDL and Triglycerides. Ouch! One study basically found that oat bran improved every lipid parameter and wheat worsened it. Check out the abstract's commentary below:"
"Time-by-treatment interactions (P < 0.05) for LDL cholesterol (oat: -2.5%; wheat: 8.0%), small LDL cholesterol (oat: -17.3%; wheat: 60.4%), LDL particle number (oat: -5.0%; wheat: 14.2%), and LDL:HDL cholesterol (oat: -6.3%; wheat: 14.2%) were observed. Time-by-treatment interactions were nearly significant for total cholesterol (oat: -2.5%; wheat: 6.3%; P = 0.08), triacylglycerol (oat: -6.6%; wheat: 22.0%; P = 0.07), and VLDL triacylglycerol (oat: -7.6%; wheat: 2.7%; P = 0.08)."
And notice that the wheat increased the all-important LDL particle count! Those who have been doing a fair amount of reading on the subject will know that it is actually the LDL particle count that is even more important than total cholesterol or LDL itself. Wheat increased this number and if you get that particle count high enough, it will literally "push" the LDL particles into your arterial walls.
Notice also that it shifted the whole lipid profile in the direction of "pattern B,"i.e. more VLDL, small LDL and triglycerides. These are all the most plaque-forming lipids and, coupled with the higher particle count, could spell trouble.
This goes right along with wheat's ability to spike blood sugar and insulin. Wheat has a uniquely high percentage of the type of starch that breaks down quickly and can spike blood sugar. In my opinion, all wheat should be considered high glycemic - even whole wheat.
4. PRO: Provides Cholesterol Oxidation Protection. In fairness to wheat, it does probably provide some proteciton against LDL oxidation.  Remember that it is oxidized LDL that is the bad boy of the cardiovascular world.
The clear message from the above studies when it comes to lipid management and control?:
Any grain but wheat!
Both oat bran and barley soundly beat wheat and we little doubt that almost any other grain would do the same.
NOTE: I emphasize the importance of it being oat bran and not oatmeal, especially instant, which can spike blood sugar post-meal in some men.
1) The Journal of Family Practice, 1991, 33(6):600-608, "Randomized, controlled, crossover trial of oat bran in hypercholesterolemic subjects"
2) Am J Clin Nutr, Oct 1991,54(4):678-683, "Lipid responses of hypercholesterolemic men to oat-bran and wheat-bran intake."
3) LWT - Food Science and Technology, Aug 2005, 38(4):463 470, "Inhibitory effects of wheat bran extracts on human LDL oxidation and free radicals"
4) Am J Clin Nutr, May 1991, 53(5):1205-1209, "Barley and wheat foods: influence on plasma cholesterol concentrations in hypercholesterolemic men"
5) Am J Clin Nutr, Aug 2002,76(2):51-358, "High-fiber oat cereal compared with wheat cereal consumption favorably alters LDL-cholesterol subclass and particle numbers in middle-aged and older men"