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A person infected with Ebola is very contagious during the period they are showing symptoms. The CDC recommends casual contact and droplet precautions.
Note the following description of (casual) contact:
(Much more contagious than an STD.)
But Lumifer is also correct. People without symptoms are not contagious, and people with symptoms are conspicuous (e.g. Patrick Sawyer was very conspicuous when he infected staff and healthcare workers in Nigeria) and unlikely to be ambulatory. The probability of a given person in West Africa being infected is very small (2000 cases divided by approximately 20 million people in Guinea, Sierra Leone and Liberia) and the probability of a given person outside this area being infected is truly negligible. If we cannot contain the virus in the area, there will be a lot of time between the observation of a burning 'ember' (or 10 or 20) and any change in these probabilities -- plenty of time to handle and douse out any further hotspots that form.
The worst case scenario in my mind is that it continues unchecked in West Africa or takes hold in more underdeveloped countries. This scenario would mean more unacceptable suffering and would also mean the outbreak gets harder and harder to squash and contain, increasing the risk to all countries.
We need to douse it while it is relatively small -- I feel so frustrated when I hear there are hospitals in these regions without supplies such as protective gear. What is the problem? Rich countries should be dropping supplies already.