Is the COVID-19 vaccine effective?

Yes. The Pfizer vaccine efficacy was 52% after the first dose and 95% after second dose. The Moderna vaccine shows similar results.

Sources and more information:

https://www.bmj.com/content/371/bmj.m4826

https://www.nejm.org/doi/full/10.1056/NEJMoa2035389

https://www.npr.org/sections/health-shots/2020/12/15/946554638/fda-analysis-of-moderna-covid-19-vaccine-finds-it-effective-and-safe