In general (key word), most people with diabetes can work in some "sugar" into their meal plan in moderation. Since ANY kind of carbohydrate will raise blood sugar levels, ALL carbohydrates must be accounted for, not just sugar.
For example, if a package says:
-10 grams sugars
-30 grams carbohydrate
-1 gram fibre
The total amount of "nutrients" that will affect your blood sugar will be 29 grams in the form of carbohydrates (total carbs *including* sugars). Fibre is subtracted out because it does not raise the blood sugar.
The reason why this is important is: If you eat something that says 2 grams of sugar, but has 29 grams of carbohydrate total, it will raise your BG eventually to the same level that the first example, with 10 grams of sugar will. The total amount of carbs determines how much your blood sugar will rise, and the "simple sugar" amount really determines how fast you will spike.
How you view all of this really depends somewhat on which type of diabetes you have. Although avoiding spikes is good for all, someone with Type 1 will have to take insulin for ANY carbs they eat, whether it comes from a piece of candy or a glass of milk. With the new insulin analogues, and the fact that insulin can be given earlier than usual so that any spikes are minimized, nothing is really "off limits" if you are otherwise in good control. The pump also offers options like temporarily increasing your basal rate with a reduced bolus to offset a spike. Thanks to new technology, Type 1's today have a lot more dietary freedom than before, and most follow a normal healthy diet with regular treats when they really want them. The key is moderation. Please note that if you also have developed insulin resistance as a Type 1 ("double diabetes"), or are an insulin using Type 2, you should follow a stricter meal plan as a typical Type 2 would.
Any excess insulin to cover "treats" will make an insulin resistance problem worse.
Someone with diet controlled Type 2 diabetes may be able to make their own insulin just fine, but since they are insulin resistant, avoiding simple sugars are more important to reduce spikes (which create more resistance, and take awhile to decrease on their own).
The issue with any form of simple sugar (table sugar, juice, pop, candy, etc.) is that it will spike your blood sugar levels quickly. If you want to avoid this, look for foods with lots of fibre, and not a lot of simple sugars. *Total carbohydrate* and calories is also very important. It is also important to note that fat and protein will decrease spikes. However, both are forms of potentially excess calories and protein can raise blood sugar levels in large amounts. You also don't want to add extra fat to your meals, unless it is the "good" fats like olive oil. The key is moderation. Everyone is different, but with trial and error, most people are able to figure out a plan that works for them. Some people are able to work some forms of simple sugar into their meal plan and have no problems, others cannot.
On the Splenda note: Most people have no problems with Splenda, and it is marketed as a "no calorie" sweetener, meaning it will not raise blood sugar levels. It has also been approved as safe with no side effects. That is my "politically correct" statement.
However, some people with Type 1 (myself included) have noticed a steady rise in blood sugar hours after consuming it. The reason for this may be that often sugar alcohols and fillers like maltrodextrin are added to granulated Splenda, both which can affect blood sugar. However, I have had this problem with all forms of it. I believe I can break down the chlorine bonding

Splenda is made by bonding a glucose molecule to a chlorine molecule so the body doesn't recognize it as sugar.
I also noticed that I seem to have an "allergic" reaction when I consume Splenda. My heart races, I feel like I'm going to pass out (I assume due to blood pressure fluctuations), I develop a headache, and I feel fatigued. Not to mention the high blood sugar hours later. So I *personally* don't use it anymore. In fact, I avoid it like the plague! I use Stevia, an all natural non-caloric sweetener from the health food store, or work regular sugar into my diet (I'm a Type 1).
For most people however, Splenda is a fine alternative, and most have no issues with it. If you are concerned about artificial sweeteners (the ever ongoing debate I won't touch), I suggest using Stevia. Do note that Stevia can lower blood pressure, so people who take blood pressure medication should clear it with their doctor and/or limit their usage. Not like that's usually a bad side effect though!
