Yes, computers do have a negative effect on family and social relationships, with the social aspect of our lives being the most affected. This is mainly because man or human beings are naturally social beings. Thus man has an innate capacity to interact with other people socially, an aspect whose development largely determines what sort of a person one grows up to be.
This can only happen when an individual interacts with other people and learns from them vital social skills such as speaking in different ways, reading and using body signs to communicate in different social set ups like family gatherings, parties, school environment, office environment and many more.
For all that to happen, one needs to spend a considerable amount of time interacting with other people. Therefore spending time on the computer which is a programmed machine means that individual is withdrawn and kept away from family and friends. This also means that the social bond that one creates, enjoys and shares with family and friends is severed because that can only result from shared appreciation, acknowledgement, endorsements such as compliments, jokes and disappointments that are mostly spontaneous and dependent on the situation on the ground like during social gatherings, sports activities and get-togethers.
Likewise an individual who spends most of his time behind a computer is likely to exhibit social withdrawal syndrome signs and anti-social behaviour such as irritability, since emotionally, the individual tends to feel uncomfortable in a group of people who may joke at him, ridicule or challenge him on an issue he is not comfortable about as face to face conversations always are guided by what an individual feels about the other person yet prolonged use of the computer tends to isolate an individual from the real world and transporting them to a fantasy world which is make belief and in which emotions count for very little, as such one ends up with compromised social skills.
People may argue that computer games are a source of great entertainment and provides an enjoyable escape from a typical day, but I find such an argument a bit flimsy since in the process of enjoying that, one is derived valuable time to share and have social skills with others which is a very imperative aspect of human development for this can be gained by interacting with others. It is said that like iron sharpens iron so man sharpens man. For instance the only way for an individual to learn to be patient is to interact with people, get heart broken and disappointed, think that they’re not your friends but in the long run get to learn that it is part of life.
Again use of the computer affords an individual very little time for any physical activity or exercise yet the human being is body, mind and the spirit. This leads to an imbalance of the well being of the individual leading to health complications such as obesity or stress related injuries due to much padding on the mouse and keyboard, back problems owing to much hours spent sitting on the computer desk, lack of sleep since computer use is naturally addictive, yet lack of sleep is itself associated with other health complications like depression that can cause lack of concentration at work place maybe even dismissal, or poor immune system or just poor physical body condition. Socially, it can also lead to failed marriages since the best way to ensure a healthy marriage is top spent time together  as a couple yet one or both spouses are spending most of their times behind the screen.
Other schools of thought argue that computers are a super way of introducing children in to the next world, the world of technology. Well and good actually this affords them a whole world of learning complete with a whole lot of exploratory possibilities. However the excessive options both in software or online activities exposes the young ones to other grave dangers, inappropriate language and discussions some meant exclusively for adults, predators and rude and pervasive people who may introduce them malicious ideas and other poor and indecent behaviour which given their fast and quick to grasp formative minds  may want to emulate hence end up with destructive behaviour, desensitized inclination  to vices such as violence, warped ideas on sexuality from watching uncensored pornographic series as well as distraction from real life which may make them forget their real obligations such as homework and household chores and keep them away from the world of social interaction and personal development. Moreover over reliance on computers especially to learning and teaching aid leads to a situation where a student can download works without necessarily solving or research which leads to lazy students, as such a habit does not allow them the chance to intellectually engage their minds consequently killing their creativity.
Over reliance on computer use can also lead to identity theft. For instance using a social networking site, one can easily misrepresent facts about himself leading to further social harm.
It is in this light that whereas the gains from invention and use of the computer cannot be underestimated, it is also in order to say that computers have adverse, negative effects on family and/ or social relationships.

1.    Computer Games effects on Kids: Ashley Haugen.
2.    How Computer Addiction Works: E.D. Grabianowski.