This question is related to and emerged from a comment by the OP on whether plastic surgery was allowed. I think the question of which parameters allow us to engage in action/dangerous sports has merit. We can all agree that some sports (e.g., Formula 1 racing, sky-diving, boxing) are more dangerous than others, and as mentioned in a comment are not necessities.
So to what extent is a Jew allowed to engage in such activities?
There is no clear cut ruling on the topic but it emerges that it is generally prohibited to put oneself at risk without a good reason (e.g., earning a living) although the parameters of this risk are not clearly defined
The basic sources are
The Rambam has two lists of dangerous things, Hilkhot Deot 4.1 has unhealthy, discouraged but ultimately permitted activities, Hilchot Rotzeach Ushemirat HaNefesh 11:5 has dangerous and forbidden things. The Tzitz Eliezer (15:39) understands the difference to be based on their degree of danger. See Chaim Jachter in Gray Matter (vol 3, p. 18) where he writes based on this that Halacha allowed reasonable members of society to define the parameters of the prohibition to engage in risky activities; Halacha permits activities that people judge to be a tolerable risk based on the idea that Hashem protects the fools.
Now this is all relative. Here is how some poskim have applied these guidelines (sources here and here)
R Moshe Tendler (Beit Yitzchak 15:71) explains this Gemara as teaching that the Halacha defines the parameters of acceptable risky activities by what the members of a society accept as reasonable
R Chaim Ozer Grodzinsky (Teshuvot Achiezer 1:23) applies this guideline only when the danger is minimal and disaster rarely occurs
R Yaakov Ettlinger (Teshuvot Binyan Tzion 1:137, 19th century) explores the permissibility of embarking on a sea voyage or a journey across a desert. He distinguishes between an immediate danger and a long-term danger. Immediate danger is prohibited in all situations. Future danger may be ignored if it can reasonably be expected to cause no harm. It is likely that such risk is tolerated only if for the purpose of earning a living or other great need.
Noda B’Yehuda (II, Y.D. 10) rules that a person who is needy may enter into a situation of danger if it is necessary as part of his efforts to earn a living. However, anyone who acts irresponsibly and suspends himself from trees or engages in risky behavior needlessly is in violation of the Torah’s directive “Be exceedingly careful to guard your lives"
Chazon Ish writes that it does not seem that this Gemara
is offering any extension to permit entering into danger.
Rather, the Gemara is dealing with a case of climbing on a tree
or crossing a ramp. These behaviors are potentially dangerous,
but when a person does them he usually does so cautiously
and with protecting himself with taking proper safety measures.
This is true whether the person is involved in earning a
living or not. The reason this is permitted is that when a person
proceeds carefully, the risk of danger is limited. This is
permitted for anyone who acts in this manner, but outright
placing oneself in dangerous conditions remain prohibited.
Here is how Daniel Eisenberg at Aish summarizes it
The Talmud asks in several places why certain potentially dangerous
actions are permitted. It answers that a person need not avoid small
risks that are accepted by the rest of normal society without undue
For instance, since automobile travel
presents an element of danger, we might think that it should be
forbidden. Nevertheless, it is a risk accepted by society and most
people do not give much thought to the danger. Therefore, driving with
normal caution (such as wearing a seatbelt and using the turn signal)
is permitted by Jewish law, despite the inherent small risk.
The rationale for this ruling is that while we may not take
indiscriminate risks, we may go about normal activities of daily
living with the guarantee of heavenly protection. This is derived from
the book of Psalms that states: "God watches over the simple." That
is, I do not have to worry when I go outside that I may be the one in
a million to be struck by lightning. Because I can rely on the promise
that God watches over me -- as I do the simple activities of daily