Should you be working out when your sick? I routinely get this question.
The answer depends on how sick you are and what exactly it is you're dealing with. Additionally, are you the type to manufacture excuses to not workout? Have you been falling off the wagon a lot lately? If the last two questions describe you then maybe you need to get out there and train anyway.
Long term, a personal trainers objective is to prevent burnout for a client. Weights can be redundant and boring, slow progressions aren't always the biggest motivator in the world but slow and steady is typically the way to go. If you're nursing a cold then taking a small break to get fully recovered is more times than not your best bet.
If a month has gone by and you have zero momentum in your training or diet, I may recommend that its better to get that started regardless of feeling a little under the weather. Positive momentum is important, and you need to keep accumulating small victories, if you've been accumulating small losses with regularily it's time to reverse the trend.
You must be honest with yourself, and not create an uncessary excuse because you're not feeling 100%. Fatigue hits people more often than anything, thats probably not a time to skip your training but reassess your diet, sleep, rest, stress, and overall recovery methods.
Obviously, if you're clamy, puking, running a fever then you're best bet is to stay at home or go see the doc.