I independently have been casually suggesting getting the vaccine to several of my friends and family.
Immunity against any orthopoxvirus is immunity against all of them. From monkeypox to cowpox to horsepox to camelpox to Alaskapox to half a dozen things that only virologists have ever heard of to God knows what relatives are floating around the virosphere under the radar. Between their exceptionally low mutation rate, their huge genomes giving a large attack surface to T-cell reactions, and the fact that there's more than a dozen surface proteins any one of which getting neutralized kills it dead, these viruses simply can't evolve around immune reactions even on timescales of tens of thousands of years. The monkeypox outbreak probably was able to finally take off human to human in 2017 in Nigeria because of the combination of an ever growing population that has never been vaccinated against smallpox and the aging population that did get it having effectiveness against infection slowly fade on a timescale of decades. I think this pre-emption of other potential orthopoxviruses rather than smallpox or necessarily even monkeypox is the strongest argument. There is an open immunological niche left behind from the eradication of smallpox and the cessation of vaccination, just waiting for something to fill it.
It should be noted that what is being offered is the third generation smallpox vaccine, also known as modified Vaccinia Ankara. It is a live attanuated vaccine, unlike the first and second generation vaccines which are just giving you a localized vaccinia infection. Ten years of passaging in chicken cells has left the attanuated virus unable to successfully replicate in mammalian cells - it invades cells, and turns them into virus factories, but the resultant virus particles fail to successfully go through the final maturation step and are sterile. Since it doesn't establish actual replicating infection it is much much safer, but is a bit less immunogenic than the old school version. Has to be propagated in primary chicken fibroblasts, making production annoying compared to mammalian culture of ordinary vaccinia.
In addition to the benefits of the third generation smallpox vaccine in and of itself, it should also make any future doses with the old-school smallpox vaccine (which is more effective and might work for longer and is easier to grow in culture and thus more likely to be widely deployed in a future biosecurity scenario) no longer dangerous. Any immune memory to orthopoxviruses nearly eliminates the possible systemic Vaccinia infection outcomes that can happen your first time getting it. One course of what they're giving out now should be very effective against bad outcomes to any orthopoxvirus for a very long time, but I know that after a few decades regular vaccinia got a bit leaky at preventing infection outright and they regularly revaccinated doctors. In this monkeypox outbreak vaccines that were 50 years old were only somewhat effective against infection risk.
I got the vaccine this summer, as did two people I know who like me actually did qualify according to the letter of the local rules. No interesting reactions. With the local rules slackening and demand falling and monkeypox all but eradicated in North America such that getting a dose now is not taking protection from someone who may have needed it this last summer, I have already been suggesting getting it for more people I know. Of course, I am a bit of an antibody hoarder with multiple elective vaccinations in my history and even more I wish I could get, who thinks about resilience a lot.
That's mildly interesting about smallpox vaccine being unusually easy to get right now, but doesn't answer the prior question about whether one should if one could: smallpox vaccination lapsed, even though the risk of accidental/deliberate release never went away, because it does have a certain rate of side-effects. How should one think about the risk of outbreak and benefit of being pre-vaccinated and does it really lead one to do so for (non-monkeypox) reasons?
My impression from rather cursory research is that serious or long-lasting side effects are extremely rare. I would guess that most of the health risk is probably concentrated in car accidents on the way to/from the vaccine clinic. Minor side effects like "the injection site is mildly sore for a couple weeks" are common. Injection with the bifurcated needle method also produced a small permanent scar (older people often have these), although all or most of the current vaccinations are done with the subcutaneous injection method common with other vaccines and so do not produce scarring.
I naively guess that from the perspective of society at large the biggest cost of the vaccine program is the operational overhead of distribution and administration, not the side effects; and that on the personal scale the biggest cost is the time it takes to register for and receive the vaccine, rather than the side effects.
As to the benefit side of the equation, the risks of outbreak are extremely conjectural and rely on several layers of guesswork about technology development and adversarial political decisions—two areas which are notoriously hard to predict—so I don't have much to say on that front beyond "make your best guess".
The third-generation vaccine being given now was specifically developed in order to have a smallpox vaccine that was safer especially for people with health problems, and so has much less of a trade-off with conjectural benefits.
There is all the very real risk that if we enter a timeline of bioweapon warfare that the virii released will be modified explicitly to evade current immunity and make vaccine development difficult.
It unfortunately appears to be possible, whatever the true origins of COVID there existed a straightforward and inexpensive way it could have been developed as a bioweapon. The gain of function setup is so simple and cheap...
In response to the 2022 monkeypox outbreak, public health departments throughout the USA and Europe are offering free smallpox vaccines to the public. (The diseases are closely related and the same vaccine protects against both.) Demand for these vaccines was high when they first became available, but has since plummeted as monkeypox cases fell, and the vaccine is now very easy to get. I have no idea how long this situation will last.
Eligibility varies by city. In some cities, including most of California, the vaccine is freely available to anyone. In other cities the vaccine is available to anyone who has (or claims to have) traits associated with risk of monkeypox exposure, such as male homosexuality or sexual contact with prostitutes.
Most likely, getting this vaccine will never matter. However, if there is ever an accidental or deliberate outbreak of smallpox or a closely derived disease, then being vaccinated ahead of time will be very good. Considering the operational difficulty of mass vaccination campaigns, getting a vaccine before any outbreak will both protect yourself and also ease the vaccination bottleneck of society at large.