The duration (2016–09–22 to 2017–02–20) and potential breadth of information exposed is huge — Cloudflare has over 2 million websites on its network, and data from any of these is potentially exposed. Cloudflare has said the actual impact is relatively minor, so I believe only limited amounts of information were actually disseminated. Essentially, broad range of data was potentially at risk, but the risk to any individual piece of data was very low. Regardless, unless it can be shown conclusively that your data was NOT compromised, it would be prudent to consider the possibility it has been compromised.
From an individual perspective, this is straightforward —the most effective mitigation is to change your passwords. While this is on all probability not necessary (it is unlikely your passwords were exposed in this incident), it will absolutely improve your security from both this potential compromise and many other, far more likely security issues. Cloudflare is behind many of the largest consumer web services (Uber, Fitbit, OKCupid, …), so rather than trying to identify which services are on Cloudflare, the most cautious is use this as an opportunity to rotate ALL passwords on all of your sites. This will improve your security, although the primary benefit is from threats unrelated to this incident.