Generally, no, you need to use the designated consulate for your home country. Individual consulates can grant exceptions on a discretionary basis. There are a number of rules that govern this.

• Not all consulates issue visas in the first place. In many countries, only one or two consulate will issue non-immigrant visas, and even fewer will issue immigrant visas. You can find out which consulates handle what from the consulate's Web site (see the link list below).
• Only consulates in your home country are required to process your application (an exception applies to countries that do not have diplomatic relations with the US. For instance, Iranian citizens are expected to use the Rome consulate, with Frankfurt as an alternate). Most consulates will also allow local long-term residents to apply. In some other countries, third-country nationals (that is, people who don't live in the country where the consulate is located) may still ask to be processed. Most consulates, though, are too busy. Usually, consulates in Canada and Mexico are traditionally more generous than other consulates (but do be aware that if the visa is denied, you may be stuck in Canada or Mexico!)
• Certain people, such as people with prior immigration violations, must always apply in their home countries.
• If there is no consulate in your country, then there is another designated consulate that you may use. For instance, citizens from Iran can use the consulate in Rome, as well as a few others.