The symbolism surrounding a red front door is not exactly clear. In China, red means luck. In Feng Shui, a red door is usually a recipe for prosperity. In Colonial times, it symbolized that the home and its owners were welcoming. I have also heard that a red front door means the mortgage is paid off- making a red front door more of a status symbol rather than a spiritual or friendly sign.
(A red door in a neighborhood around the corner from me.)
Given that there are a few meanings tied to a red front door, I feel it best to observe the architecture first, then try to make sense of it. Take, for instance, this Colonial style home. This particular red door is probably speaking to tradition more than anything else. However, a red front door on a contemporary home is probably not there for tradition, and possibly there for luck or prosperity, instead.
In some neighborhoods, where traditional architecture abounds, the red door may be quite common. To stand out, consider other colors. Lately, I have noticed a trend for yellow front doors (yes, yellow!). Remember that your door can be a statement. It does not have to match the rest of your trim or dominant exterior color.
Door colors that I would consider experimenting with, given the proper architecture and neighborhood: deep purple, midnight blue, deep orange,
yellow (A yellow door is too fun, plus, its also my favorite color!). Really, you can use any color- so long as you get the right value (not too bright or vibrant and not too light or pastel).
If you want to experiment with a front door color, but you are nervous to make a bold statement- start with a color that is already part of your house's exterior, just go a lot deeper. If you have a light blue house, consider navy blue or black. If you have a tan house, try rich chocolate brown or any other deep earthy color such as forest green or a burnt sienna brown.
Just be sure to consider your house's architectural style and go from there. A colorful, statement making front door is a sure way to set your house apart while implementing a fresh take on tradition.