I usually think about lineages from the perspective of the ancestor. E.g. my grandpa had 5 kids; those 5 kids produced 9 grandkids; those 9 grandkids produced 3 great-grandkids (so far); 17 descendants in total.
Over the last few days, I've been having fun thinking about the situation in reverse, from the perspective of the descendant. Here's a quote from Genes: A Very Short Introduction by Jonathan Slack:
Also, when considering 'roots', some of the basic mathematics of inheritance needs to be borne in mind. With fully random matings the number of your ancestors doubles every generation. Ten generations ago (250-300 years) we might expect about 1,000 ancestors each contributing 0.1 percent of their total variants to your genome... when the number of ancestors exceeds 2,000-3,000 (12 generations would be about 4,000), it is likely that some ancestral sections of DNA have been lost altogether... by about 15 generations back many of the ancestors contribute no DNA variants at all but they are still ancestors on the lineage. So, even though we all have an ancestry running back to the origin of life on Earth, we do not necessarily have any DNA variants from most of our ancestors.
(In the original version of this post I did a thought experiment here to calculate when the number of ancestors starts to get nonsensical, i.e. if you double the number of ancestors every generation there's a point where the number of ancestors exceeds the total number of humans at that point. I've removed this thought experiment because I think it distracts from my main idea. See the Hacker News discussion.)
Your exact number of ancestors depends on how much pedigree collapse there is in your lineage, but I'm pretty sure the basic premise of this blog post holds: you've got a lot of ancestors.