Lately I've heard a lot of discussion about whether things will ever go back to normal. My answer is: It really depends on what you consider "normal."
I've seen political ideologues of all stripes claiming that their time has come: Right-wing militia types believe this will bring about the civil war they've been preparing for. Libertarians believe this will cause the government to trim away unnecessary regulations. Socialists and anarchists believe this will bring about the end of capitalism, either due to economic collapse or simply because it makes people realise that capitalism doesn't work. I've also seen some leftists go the opposite route and claim that this crisis will result in a fascist takeover, plunging the world even deeper into right-wing authoritarianism. Needless to say, I'm reasonably certain none of that is going to happen. If your definition of normal simply means "there won't be a complete upheaval of the political and economic system," then yes, things will almost certainly remain normal.
That doesn't mean there won't be some major changes. For one thing, there's going to be an economic recession. It was bound to happen sooner or later, but the pandemic hastened the process and likely made it worse than it would've been otherwise. It may be even worse than the 2008 financial crisis. Still, it won't be the civilisation-ending disaster that some are expecting, or even on par with the Great Depression. The economy will recover in the years to come, though a complete recovery may take 5-10 years (possibly longer, if quarantine measures remain in place for a year or more).
In the US, we're likely to see some major reforms to the existing healthcare system, and possibly even the implementation of universal coverage (either through a single-payer system or, more likely, a government-funded multi-payer system like Germany's). Countries around the world will also take measures to be better prepared for future pandemics. This will probably entail an increase in funding to biomedical research, disease prevention organisations, and healthcare services to enable a faster mobilisation and response time.
There's also a slim chance that some countries or states might implement Universal Basic Income: Many places are already giving citizens/residents what amounts to a temporary UBI for the duration for the quarantine, and if this system seems to work out, it could become permanent. I'd say the odds are low, although the longer the quarantine lasts and the more people get used to living off a government stipend, the more likely it is to stick around.
There are also plenty of more subtle changes, many of which aren't political at all. Working from home will become a lot more common for a lot of white-collar jobs; it's more comfortable for employees and more profitable for employers, there's really no good reason we weren't doing it already beyond tradition and office culture. Large-scale social gatherings will become less common, video calls and teleconferences will become more popular. The trend of urbanisation may start to reverse, with more people moving out of the cities and into suburbs or semi-rural areas. (In fact, the trend was already starting to reverse before the pandemic, largely due to the prohibitively high costs of living in major cities; this will simply exacerbate the process.) And I'm sure there will be plenty of other social, cultural, and logistical shifts that I can't predict.