In your 3d application your model will always stand nicely on it's feet, but if you don't take care your REAL model might just keel over – you'll need to examine the location of your object's center of mass in relation to the size and location of the contact points with the floor.
If you're lucky, your 3D app may have some kind of physics simulation or center of mass calculator that you can use. If not, here's a trick I like to use:
Draw a curve around the contact points of your object with the floor. Next, take a look from the top of your model and see if the bulk of its mass fits inside this curve. If it does, it'll be pretty stable. If it doesn't then you may want to take some additional steps (see below).
Also take the shape of the contact area into account: it should be circular-ish.
Here's an example. Cornelius here has a big head and a fat tummy, but only two very tiny feet. The red area is the curve that I drew around his feet. In the image on the right you'll see that the contact area is very small compared to the entire character.

As a result, the contact area is now MUCH larger and the resulting printed model will be rather stable.
The height of the object is of course also a factor: higher objects will be more unstable. Take another look at the position of your center of mass. Next, measure the average size of the contact area. A good rule of thumb is that these two sizes should be roughly the same.
In the case of Cornelius, I estimate that the the center of mass is about at the height of his arms. This relates nicely to the size of the contact area so I'm still confident that this character is stable.
Examples of this method:
- 'Petunia' here can stand, but as her mass is too far to the front, she turned out quite unstable.
- 'Toon Hen' has nice big feet that are well placed with respect to the center of mass: