Since English physician Edward Jenner first inoculated a 13-year-old boy with cowpox (or the vaccinia virus) in 1796 and the subsequent development of the first smallpox vaccine a couple of years later, a number of vaccines have been created to prevent disease such as typhoid fever, tuberculosis, and polio that could have previously proven dangerous or fatal.
According to the World Health Organization, immunization currently prevents 2-3 million deaths each year.  Unfortunately, vaccine-preventable diseases still cause 1.5 million deaths each year as well. 
By receiving on-time vaccination, individuals not only build immunity to certain pathogens themselves, but contribute to herd immunity for those who cannot be vaccinated. In turn, infectious diseases are less likely to spread and populations are generally healthier. Healthier children perform better at school and healthier adults are better able to tend to their families and be more productive at work. At the societal level, healthier peoples “may be a stronger magnet for foreign direct investment and tourism than those where diseases pose a constant threat.” 
In a 2018 study conducted by Wellcome, 92% of people worldwide believed that vaccines were important, 79% agreed that they were safe, and 84% thought they were effective.  However, an earlier study published in 2014 suggests that “hesitant attitudes to vaccination are prevalent and may be increasing since the influenza pandemic of 2009.” 
Interestingly, this topic is even more timely with the emergence of the COVID-19 pandemic and the new Pfizer-BioNTech and Moderna vaccines. Uncertainty toward being immunized seems especially widespread now, evidently most likely due to the speed at which the two vaccines (and others in their final stages of testing) were created, tested, and deployed.
While vaccine development and approval by the Food & Drug Administration (FDA) can usually take anywhere from 10 to 15 years in the United States, the COVID-19 vaccines were granted an Emergency Use Authorization – but only after being rigorously tested in the same manner that scientists regularly adhered to. 
That is to say, the Pfizer-BioNTech and Moderna vaccines still went through a pre-clinical period, followed by three separate phases of clinical trials involving tens of thousands of participants, and a regulatory review before receiving approval and being widely distributed.
This was made possible due to certain differences between our current situation and the timeline that most prior vaccines followed:
[M]odern scientific tools are faster than old ones, and there was a worldwide effort to reduce or remove the usual barriers and delays in vaccine research, production, and distribution. A large number of ordinary people volunteered for clinical trials of the vaccines, which meant we got the answers to key questions about safety and protection quickly. 
It should also be noted that the Pfizer-BioNTech vaccine is “95% effective at preventing symptomatic Covid infection, measured starting from seven days after the second dose was administered,” and that the Moderna vaccine is 94.1% effective, measured starting from 14 days after the second dose.  When compared to the flu shot’s average of ~40% effectiveness, these numbers should be encouraging.  Even so, rationales against vaccination still exist:
Support for anti-vaccination generally falls into three categories of exemption: religious, philosophical, or medical.
Catholicism views immunization as “sharing the evil intention”  in how vaccines are prepared, namely those “using cell lines derived from a voluntary aborted fetus.” 
Certain Orthodox Protestants believe that the act of vaccination obstructs providence and maintain that “man is not allowed to cause disease in a by God given healthy body.”  Additionally, experiencing any side effects from being immunized is seen as a sign of God that a person had made the wrong choice.
From a Jewish standpoint, some refuse vaccination on the groups that they may contain porcine and gelatin components, going against their belief in “eating only animals that both chew their cud and have cloven hooves.” 
Muslims may also reject vaccination because the use of “flesh of swine” and gelatin made from other animals (depending on how they died) is forbidden. 
Philosophical reasons for avoiding immunization include conscientious objection, personal moral code, and conviction in individual freedoms.
Medical issues such as allergies, Guillain-Barre Syndrome, seizure disorders or a history of seizures, a weakened immune system, pregnancy, and age are also valid justifications for declining or delaying vaccination. 
For example, the risk of having a febrile seizure “increases 2 to 5 times on the day of administration of an inactivated vaccine and on days 5 to 14 following a live attenuated vaccine,” with one study concluding that 65% of children that had seizures or developed epilepsy following vaccination had underlying causes for having a seizure disorder.  Furthermore, fever and infection (complications that may result from immunization) are known triggers for seizures in epileptics. 
For those with weakened immune systems, there is a possibility of vaccination causing an infection, or, depending on the severity of suppression, that the immune system “might not fully respond to the vaccine.” 
As demonstrated here, there are some justifiable motives for denying or delaying vaccination; nevertheless, it should be noted that in most cases listed here it is feasible for a person to be immunized at a later time or for a different vaccine to be used.
 World Health Organization, “Immunization coverage,” last modified July 15, 2020, https://www.who.int/en/news-room/fact-sheets/detail/immunization-coverage.
 Samantha Vanderslott, Bernadeta Dadonaite, & Max Roser, “Vaccination,” last modified December 2019, https://ourworldindata.org/vaccination.
 David E. Bloom, David Canning, & Mark Weston, “The Value of Vaccination,” World Economics 6, no. 3 (July-September 2005): 15-39, https://lnct.global/wp-content/uploads/2017/10/David-E-Bloom-The-value-of-vaccination.pdf.
 Wellcome, Wellcome Global Monitor 2018, (Gallup, 2019), https://wellcome.org/sites/default/files/wellcome-global-monitor-2018.pdf.
 Ohid Yaqub et al., “Attitudes to vaccination: A critical review,” Social Science & Medicine 112 (July 2014): 1-11, doi: 10.1016/j.socscimed.2014.04.018.
 U.S. Food & Drug Administration, “Emergency Use Authorization for Vaccines Explained, last modified November 20, 2020, https://www.fda.gov/vaccines-blood-biologics/vaccines/emergency-use-authorization-vaccines-explained.
 Kara Gavin, “Not Sure About the COVID-19 Vaccine? Get the Facts, Then Decide,” Michigan Health, December 23, 2020, https://healthblog.uofmhealth.org/wellness-prevention/not-sure-about-covid-19-vaccine-get-facts-then-decide#speed.
 Helen Branswell, “A side-by-side comparison of the Pfizer/BioNTech and Moderna vaccines,” STAT News, December 19, 2020, https://www.statnews.com/2020/12/19/a-side-by-side-comparison-of-the-pfizer-biontech-and-moderna-vaccines/.
 UCDavis Health, “How the COVID-19 vaccine works, potential side effects and more, last modified January 26, 2021, https://health.ucdavis.edu/coronavirus/covid-19-vaccine/how-covid-19-vaccines-work.html.
 E. Sgreccia, Moral reflection on vaccines prepared from cells derived from aborted human foetus, (Pontificia Academia Pro Vita, June 2005), https://drgreenmom.com/wp-content/uploads/2014/01/Vatican-Statement-on-Vaccines-Derived-from-Human-Fetal-Tissue-PDF.pdf.
 Gordana Pelcic et al., “Religious exception for vaccination or religious excuses for avoiding vaccination,” Croatian Medical Journal 57, no. 5 (October 2016): 516-521, doi: 10.3325/cmj.2016.57.516.
 Wilhelmina LM Ruijs et al., “How healthcare professionals respond to parents with religious objections to vaccination: a qualitative study,” BMC Health Services Research 12 (2012): 231, doi: 10.1186/1472-6963-12-231.
 Andrew Wolfson, “Seven facts about keeping kosher,” Courier journal, July 22, 2016, https://www.courier-journal.com/story/news/crime/2016/07/22/seven-facts-keeping-kosher/87456202/.
 John D Grabenstein, “What the world’s religions teach, applied to vaccines and immune globulins,” Vaccine 31, no. 16 (April 2013): 2011-2023, doi: 10.1016/j.vaccine.2013.02.026.
 Centers for Disease Control and Prevention, “Who Should NOT Get Vaccinated with these Vaccines?,” last modified April 2, 2020, https://www.cdc.gov/vaccines/vpd/should-not-vacc.html?CDC_AA_refVal=https%3A%2F%2Fwww.cdc.gov%2Fvaccines%2Fvpd-vac%2Fshould-not-vacc.htm.
 Ingrid E. Scheffer, “Vaccination Triggers, Rather Than Causes, Seizures,” Epilepsy Currents 15, no. 6 (2015): 335-336, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4657773/pdf/i1535-7511-15-6-335.pdf.
 Karina A. Top et al., “Risk of seizures after immunization in children with epilepsy: a risk interval analysis,” BMC Pediatrics 18 (2018): 134, doi: 10.1186/s12887-018-1112-0.
 Liza Torborg, “Mayo Clinic Q and A: Should you get vaccinations with a suppressed immune system?” Mayo Clinic, October 22, 2019, https://newsnetwork.mayoclinic.org/discussion/mayo-clinic-q-and-a-should-you-get-vaccinations-with-a-suppressed-immune-system/.