I have started a family tree, starting with myself and working back in time. As I climb up the tree, how far from the direct line is considered a relative?
It's a matter of preference since there is no strict cut-off. Many people will follow their own surname through previous generations, or a small group of surnames, although surnames are not really significant from a genetic or lineage point of view.
I follow both surnames at each generation (i.e. paternal and maternal lines), and basically go back as far as records allow me to. For each of those lines, I also project fowards in order to find the siblings, cousins, and related descendants. In effect, each ancestral line is a family tree in its own right.
This may sound like a huge task but the advantages are in finding "distant relatives" who may be able to help with missing history, important citations, copies of documents, photographs, etc. Since I'm researching family history, rather than just genealogy, then those extended families can often be very significant.
The relevant dictionary definition of relative is "somebody connected by blood or marriage", so strictly speaking anyone that you can navigate to on a family tree starting from yourself is a relative. (I'm ignoring here the possibility that your genealogy database contains unconnected people.)
However, some links are so distant you may decide that time (or life) is too short to pursue them, unless there is a visible advantage — such as sharing research efforts with distant cousins into a common ancestor, or investigating DNA-testing results.
I choose to work backwards as far as I can go on all my direct ancestors (i.e. everyone from whom I am descended), but also to follow siblings of my relatives and their children forward for two-to-three generations (or more, if I find something interesting). This increases my possibilities for making contact with cousins, but also I've found on a number of occasions that cousins in the past end up migrating to the same town/district of a city and it can be very helpful to know the connections between people of different surname who are in fact related.
The idea of a "relative" is as much a social concept as it is genealogical. It often carries meaning concerning being acknowledged or recognised as part of a family or clan. How broadly you extend that recognition is often a very personal decision.
I know of families whose members can list the names of second and third cousins and would consider all of them to be close relatives. I also know a man who refuses to acknowledge his own brother.
We cannot choose those with whom we share genes (and ancestors). We do decide who we relate to on a personal level. Family historians need to make the same choices when studying generations past. Your seventh cousin three times removed is part of your family, but that does not mean that you must be interested in her life.
'Relatives' are 'relative'. What is the context of the question? Your direct ancestors are all 'blood relatives' by the definition:
blood relation n. A person who is related to another by birth rather than by marriage.
According to US Gov (for purposes of employee benefits), the definition of an 'immediate relative' is:
Immediate relative means an individual with any of the following relationships to the employee:
Spouse, and parents thereof; Sons and daughters, and spouses thereof; Parents, and spouses thereof; Brothers and sisters, and spouses thereof; Grandparents and grandchildren, and spouses thereof; Domestic partner and parents thereof, including domestic partners of any individual in 1 through 5 of this definition; and Any individual related by blood or affinity whose close association with the employee is the equivalent of a family
One is very broad. One is fairly narrow. Family reunions are somewhere in-between. Lineage society 'cousins' generally meet the 'blood relative' definition.
From a common DNA viewpoint, it halves with each generation so it's a gradual lessening. You have 23 chromosomes and you get half of each one from each parent. You can do the math to determine the probability you happen to have one of their chromosomes. The math is easy for Y chromosome for direct male line and mitochondrial DNA for direct female line. For the rest, it's probabilistic. So don't feel remote from your mother's mother's .... mother. Every cell in your body has her mitochondrial dna in it.
A study by a Columbia University researcher suggests that Ashkenazi Jews are all at least 30th cousins: http://www.livescience.com/47755-european-jews-are-30th-cousins.html You can read the scientific study here http://www.ncbi.nlm.nih.gov/pubmed/25203624
Genetic tests can show ancestral origins for tens of thousands of years. But as far as actually tracing relatives through genetic testing as we have today, DNA relatives start dropping off our tree after 5 generations or so, according to current genetic genealogy testing companies.
Personal preference. I don't include all siblings unless i'm trying to get to a particular historic figure - I do go thru siblings back two generations to include my mother's aunts, uncles and first cousins - those she knew and I heard her talk about. So for me direct ancestors but in most cases siblings back two generations prior. Could, should do more but that's my way to keep things in some degree of focus. I try to play fair with paternal and maternal lines - follow them equally where they lead.