The US very often offers aid, in cases of disaster as mentioned by Oldcat, but also to countries that are having economic or security issues. As pointed out by Semaphore the answer to the question is: No, not all countries that exist/ed at the same time as the US have been offered aid to
I also think it's important to understand what exactly is "aid" between governments and this isn't exactly what you would call "helping your friend".
Usually, when accepting aid, recipient countries can only spend the money in certain ways, with certain companies, from certain countries, often to the disadvantage of the aid recipient. An example:
However, non-government organization watch groups have noted that as
much as 40% of aid to Afghanistan has found its way back to donor
countries through awarding contracts at inflated costs.
So the donor country's economy benefits from these deals, and the recipient also has to pay it back eventually: "Double profit" for the donor. And if the recipient can't pay it back, well that may even be better for the donor. The recipient is now indebted towards it...
Other times, aid is given as a covert way of undermining unfriendly governments:
In situations where the U.S. is hostile to the government of a
country, USAID may be asked to undertake programs that the government
would not accept and thus to operate without the government's
knowledge. This might include USAID support for opposition political
movements that seek to remove the government. Such "political aid" is
criticized by some as being incompatible with USAID's role as an
assistance or cooperation agency and as exposing USAID staff worldwide
to the suspicion of being covertly engaged in subversion.
Aid recipients are also expected to align themselves politically with the donor:
In 1990 when the Yemeni Ambassador to the United Nations, Abdullah
Saleh al-Ashtal, voted against a resolution for a U.S.-led coalition
to use force against Iraq, U.S. Ambassador to the UN Thomas Pickering
walked to the seat of the Yemeni Ambassador and retorted: "That was
the most expensive No vote you ever cast". Immediately afterwards,
USAID ceased operations and funding in Yemen.
Wikipedia with sources for all three citations and other examples there
Recently, many recipient countries are taking steps to minimise or terminate USAID programs in their countries. USAID has a particularly bad reputation in South America, where ALBA countries are demanding it cease operations, and the Middle East:
It is a bit naïve to think that large powerful governments can allow themselves to be altruistic. Usually their job is to work for profit, economical or political.