First of all note that the verse part saying a male inherits twice of what a female inherits apply to brothers and sisters only, so it isn't a general ruling in shari'a.
Also note that in shari'a the shares of the women are specified and given a leading position they are called أصحاب الفروض ashaab al-Forod those with a specific share (the counterpart is called العصبات al-'Asabat and they are of three categories and all are male or at least offspring of male), so in presence of a female her share is taken in account in first place. Of course some males are also among ashaab al-Forod. The shares of men however may increase after considering all primary shares by distribution of the rest of the heritage!
This seemingly injustice (I especially mean the fact that a male can have more than his prescribed share, but also the cases where men inherit more than women) is of course -as many if not all of the given answers say- due to the fact that a woman is not asked to pay mahr nor to be in charge for her family while this is the man's duty according to shari'a!
In this link I found a hint of an answer with another indication of what I've heard their it is said that:
Women only inherit half of the share of men in 4 cases, while they inherit in 11 cases the same as men, in 14 cases they inherit more than a men and in 5 cases they inherit while a men doesn't!
So basically a woman can inherit:
- less than (more exactly the half of) a male: for example if there are sisters and brothers, a sister gets only a half of what her brother would inherit, a mother would also inherit only one half of what the father may inherit in absence of spouses and children (of their dead child).
This applies in general in 4 cases:
a) daughter and son,
b) daughter of the son and son of the son,
c) brother and sister (same parents),
d) brother and sister (paternal). - the same of a male: like father and mother if there are children (each of them will inherit one sixth) while the son would inherit the rest, also the brother or sister of the mother would get equal parts based on:
... " And if a man or woman leaves neither ascendants nor descendants but has a brother or a sister, then for each one of them is a sixth." ... (4:12)
and this applies in cases such:
a) daughter and father, (note that the father only gets the half as there are no other heir as his real share is only one sixth)
b) daughter and son of the son (same situation the son of the son is only allowed to have the rest of the share, as there are no other heir his share would be half of the heritage)
c) daughter and a single brother (same as above the brother takes the rest)
3. more than a male: the husband with his two daughters (he would only inherit a quarter, while they would inherit two thirds, one third each of course if there will be a son this would change)
..." But if they have a child, for you is one fourth of what they leave, ..." (4:12)
the husband with his lonely daughter also would inherit much less as his share is only a quarter, while she would inherit the half and maybe the last quarter would be added to her share too.
Some other cases:
a) daughter (1/2), father (1/6 + rest) and mother (1/6)
b) daughter (1/2) and =>2 brothers (share of the rest)
c) 2 daughters (2/3, 1/3 each) and uncles (share of the rest)
- she might inherit, while her male counterpart wouldn't inherit at all: like the case of a woman who has died leaving a husband (1/4), a father (1/6), a mother (1/6), a daughter (1/2) and a daughter of a son, in this case the daughter of the son my inherit a sixth while a supposed son of the son wouldn't inherit from his grandmother as his share is the last which would be considered as the rest in this constellation, but as each of the husband, father and mother have defined shares and the daughter (as the child of the husband) has a stronger primacy than the son of a son (as he is male, but not for the daughter o the son)!
An other case is that of a daughter (1/2), a sister (from both parents) and a paternal uncle (0). Here the daughter and the sister will share the whole heritage!
Sources (Arabic only) islamqa#135065 and this article on the shares of women.