Genetics will play a role in things like your:
- Slow/Fast twitch muscle fibre ratio, but most people have about 50% slow-twitch and 50% fast-twitch fibres in their muscles, according to Physiology; training does not change the fibre ratio. But by your way of training you decide which fibres you accustom your neuromuscular system to train more.
- Your physique and Muscle Hypertrophy: The basic size of your muscles is determined by genetics and testosterone levels (which is why men have larger muscles than women). But by training your muscles can become 30-60% more hypertrophied, and there are every day things you can do to increase your testosterone naturally.
- Your metabolism: Genetics can dictate 40 to 70% of how your metabolism operates, but by adding muscle or fat you change this. Aerobics is what reduces fat in the short term, anaerobics is what reduces the fat in the long term.
- Body Composition and Fat: Genetics will determine things like fat distribution, etc. But your body composition is something that can be changed even if you are genetically predisposed to be fat. By your life style and eating habits you decide what you are.
- Muscle Fibre Density: Muscle fibre density is by definition the amount of fibres that are packed within a given volume of muscle tissue. This is what can makes other person's muscles appear more thicker, fuller than yours.
- Strength: Genetics determines your muscle belly and limb length which in turn, say...you have short limbs will have the advantage of increase leverage that will let you lift more weight. If you have longer muscles you will have increased size and strength potential over the person with shorter muscles. Muscle strength is also influenced by the point of tendon insertion, example:
Jim and John both have the same arm and muscle length. However, Jim's biceps tendon attaches to his forearm farther from his elbow joint than John's does. This gives Jim a biomechanical advantage: he is able to lift more weight than John in biceps exercises such as the Biceps Curl. Also as stated above your fast twitch fibre ratio can differ and this can effect strength as fast twitch are for the strength (explosive,power) generating forces.
- Peak bone mass. Your genes determine your Skeletal structure, which is important for size and strength. Strong bones are important for support of heavy weights. But getting calcium can help maximize genetic potential for storing calcium in the bones.
- Women and Men in Strength and Muscle size: Generally it is the testosterone that makes all the difference, Female muscle can achieve almost exactly the same maximum force of contraction as the male: 3-4 kg/cm^2 (in terms of strength per square centimeter of cross-sectional area of muscle tissue). Men will have muscles that grow 40% or more larger than the female, thanks to our testicles. ha ha!
- All that other good stuff: Height, bodyweight, body type, muscle shape, etc.
Just like you can damage your genetics(with drugs, alcohol, etc.), you can also improve upon them (with exercise, good nutrition, etc.), good genetics didn't just pop out of the blue they had to have begun somewhere. We all have genetics, so do not brag and whine if you think they suck if you are having troubles with your physique or strength, look at what you are eating, Genetics were the basic frame work; but food really made us what we are today. It is your choices if you will be muscular, fat, strong, or weak, not your genetics, your genetics don't lift weights, you do!
Don't set limitations! Most of the people who accomplished great feats did so because they had the drive, persistence, vision and dedication to do it. When I am in the gym I don't even think or care about my genetics.
Some reads:
http://www.drlenkravitz.com/Articles/genetics.html
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Thanks for bringing it all back. 
