1. The Dead Calm - if the wind suddenly stops it can be a sign that one has touched down and is in your area. The air will be hard to breathe in and will feel very stuffy.
2. Listen to the animals-if you normally have crickets, frogs, or other loud animals at night and you notice there is a distinct lack of sound then you should keep an eye on your area. This of course can just mean severe weather but during a tornado watch can be a sign to watch closely.
3.Finger Lightning- lightning that streaks across the sky instead of being vertical is a classic sign in some areas.
4. Hail- it often comes with tornado producing storms and if the hail suddenly stops then it can be a sign of a touchdown near by the same as a strong wind and a sudden dead calm
5. Orange Sky- while this can happen with thunder storms as well it also happens during a tornado due to the large amount of dust and dirt being picked up by the swirling winds.
6. Light Flashes at Ground Level- If there are light flashes near ground level at night of a blue green to white color in small flashes, these are signs that power lines are being torn down.
And of course always be on the look out for funnel clouds during a potentially tornado producing storm. Know your safety plan and don't panic.
(These are things I have personally been taught and have held true it may not be the same for all areas. Feel free to add your own knowledge below.)
If you have a home with a lot of windows and are unsure what the safest place is then I would recommend the bathroom. You can put small children in the bathtub and cover them with blankets, pillows, or even a small mattress.
Closets, they can be a safe place again bathrooms tend to work, take everything out of the top as quickly as you can and put your hands over your head facing the back wall of the closet.
Hallways are another safe place if you are unsure of other areas, though not as safe as the other two options they can work if you are trying to move as fast as you can.
If you are out and about and have no where else to go find a ditch and duck and cover, high sided ditches can break the winds around you and may save your life, never ever stay inside your car.
Weather Radios can be a good back up for when power is out and cell towers are down.
And from commenter rhope 4 "I'm a storm spotter in my area, and one thing I do is watch the NWS radar. Go to http://www.noaa.gov/ , type in your zip code in the window to the left under "active weather alerts." This will bring up the forecast for your area. Down the page to the left will be a radar link. Click on it. It gives you a single image, but if you look to the right of that page, you will see "composite" and "reflective." Click on the word "loop" to the right of either of those words, and it will put the radar into motion. It will be delayed by about 20 minutes, but it will give you an idea if something is headed your way if you know where you are on the map.
This is how I monitor the weather in my area, and if I see something on the radar getting close, I go outside and watch the clouds."