No vaccine is 100% effective in preventing infection. But the rate of so-called “breakthrough” cases is very, very low — less than 1%.
It should also be noted, that vaccines are not “cures.” Instead they are meant to prevent severe illness, hospitalizations, and death. They have been very effective in fulfilling these goals.
COVID vaccines have been shown to be very powerful in preventing more severe disease and the need for hospitalization. Therefore, those who are unvaccinated are at higher risk of hospitalization and death.
In February 2022, the CDC released a report showing COVID hospitalization rates were 23 times higher for unvaccinated people.
Breakthroughs have occurred more frequently recently because of the high level of infectiousness of the current variants. But people having breakthroughs generally have a much more mild infection — more like a common cold or upper respiratory infection. The vaccines prevent severe disease and complications and allow people to return to their healthy selves more quickly.
https://www.bu.edu/articles/2021/myths-vs-facts-covid-19-vaccine/ (Boston University)
https://www.nejm.org/doi/full/10.1056/NEJMoa2117995 (New England Journal of Medicine)
https://www.mayoclinic.org/coronavirus-covid-19/covid-variant-vaccine (Mayo Clinic)