I'll point out some possible situations; these are certainly not exhaustive and some can overlap, but will probably give you a better idea. Some of the terminology I'll use might be a bit US-centric, but the general principles also apply elsewhere.
Phase 1 clinical trials
Phase 1 trials are the first of four phases that make up a typical clinical trial progression. Phase 1 trials are typically not placebo-controlled, often involve healthy volunteers, and are not designed to measure efficacy or really powered to involve statistical testing at all.
Instead, they are mostly dosing studies and preliminary safety studies. They look for severe, unexpected outcomes for safety. For drug trials, they often involve measuring the pharmacokinetics of different doses to compare to preclinical data and to help set dosing strategies for future trials.
Studies evaluating a standard of care
These sorts of studies are meant to describe outcomes under current care rather than make a comparison, and can also include studies using data in clinical registries.
Clinical registries collect data on a group of people which are then used to make comparisons later, contact people for enrollment in trials, etc. Sometimes you may design such comparisons with some sort of internal control group, but there is no pre-specified control and experimental group and no randomization. They are useful in tracking outcomes in more real-world situations to understand the scope and prognosis of a disease.
Exploratory/descriptive research
Lots of medical research is exploratory or descriptive rather than comparative. If there is no intervention to focus on, there may not be a need for a control group, or it may be possible to use historical controls. Case studies would be a subset of these, where an individual case is the basis of a report.
A lot of these descriptive studies have been part of the early published research around the COVID-19 pandemic. Since it's a new illness, people want to know things like how many people infected die, how many need to be on a ventilator, etc. Such studies might use other groups sort of like "historical controls" for comparison, like seasonal influenza or the original SARS, but they don't typically do a statistical comparison between groups, they use descriptive statistics like means or proportions with confidence intervals.
Compassionate and off-label use
Compassionate use of unapproved drugs, or off-label use of drugs approved for other indications, is sometimes an alternative to clinical trials in trying new treatments. When no known treatment exists or when other treatments have failed in a given patient, a treating physician can have broad discretion in treatment on their own, rather than under the umbrella of a clinical trial. Data from compassionate use isn't typically used to support drug approval - there are substantial ethical concerns - but it can be used to motivate further research and other physicians may use positive reports from compassionate use cases to try the same treatment in their own patients. This is the scenario closest to the urgent situation you describe.
Placebos vs other types of control groups
I've focused mostly on circumstances where neither placebo or a proper control group is used, but I also wanted to point out that control groups often include active controls, like a current standard of care, or use historical data as a control group, such as comparing outcomes before and after some change in the standard of care. Often a placebo intervention is considered unethical when there is already a standard of care known to be effective.
