What would happen if two different viruses penetrated one cell?
One infected cell may produce hundreds of new viruses. By the time the disease occurs, many thousands of cells may be infected and producing new viruses. These new viruses are released from the cell, often in bunches, and are almost identical. Sometimes the host cell makes mistakes in copying the virus nucleic acid, causing some genetic variation. However, the outsides of these new viruses tend to be pretty much all the same, and they will usually infect only some more of the same kind of cells that produce them ¯ either in the same host animal or, if they can get out, other animals. Viruses produced in the respiratory tract are usually shed in droplets from the mouth and nose; viruses produced in the digestive tract are usually shed in feces but sometimes also in vomitus. 

One person or animal is usually infected with only one kind of virus at a time, so the bunches of virus they produce and shed are all the same. Then, if this virus infects another person, even if two of the same kind of virus bump into a single susceptible cell, the infection will still be all of one type. However (much less likely), if viruses from two different infections get mixed up in the air or in sewage and get into a single person, it is possible that two different viruses will attach to receptors on the same cell and infect that cell together. If the two viruses are closely related, their nucleic acids may "recombine" while they are being copied. When this happens, part of the genetic information from one virus is linked to the genetic information from another virus, and the new virus that is produced is a "hybrid." 

If you read about influenza that is traveling about in populations you will see that the outside of the influenza virus has an H type and an N type. For example, you might read that this year's main influenza virus is type H3N2.A reason to get a new flu vaccination each year is that the vaccine has to be made to immunize us against this type. Somewhere out in the world, a double infection as described above may happen between two different types of influenza viruses and some of the new virus may be type H5N4. Once this new type is established, a new vaccine is needed, or people won't be protected. Development and production of vaccines are expensive, and distributing them and getting people to use them is difficult. So, here is at least one situation where your question about two viruses infecting one cell may have serious public health results. Of course, influenza viruses that develop in birds, and sometimes other animals, may also be transmitted to people. Not many other kinds of viruses can jump host species like this, but it is possible that Ebola was transmitted to people from apes, perhaps from eating "bush meat." Viruses and other infectious agents that are transmitted from animals to people are said to be "zoonotic"; once this happens, the virus can usually be transmitted from person to person after that. Obviously, this too is an important public health concern.

http://www.madsci.org/posts/archives/2007-12/1198562498.Vi.r.html