Each country has different rules for obtaining visas (check out what you need to get a visa to most Southeast Asian countries, a visa to China or an Indian visa) and often applicants are required to show up at a particular embassy or consulate in person. Sometimes, the process takes multiple visits over a course of days or even a week.
While there's no way around the time requirement, there are ways to make the visa process more convenient. Nearly all travel agents in Bangkok also offer visa services. Drop off your passport, the visa fee and an extra $10 - $20 and in a few days you'll have a visa in your passport without having to trek out to an embassy or stand in a long line. Travel agents in other parts of the country sometimes also offer the service, though it will take longer and cost more as your passport will be sent to Bangkok for processing.