At that point, I considered asking him to stop the taxi so I could get out, but luckily, I remembed how to get to where I needed to go, and I could direct him the entire way. It helps a lot that I can speak some Thai. But, for foreigners who can't speak the language, taking a taxi in Bangkok can, at times, be frustrating.
Fortunately, there are some things you can do to assure finding your way around this place without a major headache. One thing you can do is to arm yourself with a map. It probably won't help to show the driver the tangled web of streets, but you can use it yourself to help navigate and tell the driver where to go. Most drivers understand some basic English, such as "turn left, turn right, u-turn, and stop", and, of course, you can always point in the direction.
Another tactic I recommend is to bring a business card of the place you're going. Make sure it includes their address written in Thai, and their phone number. Some business cards in Bangkok even have directions on them. The other approach is to have someone at your hotel, restaurant, or other tourist spot, who can speak both Thai and English, tell the driver where you want to go. Or, you could have them write down the location in Thai for the driver.
If all those things fail, and the driver gets lost, take the Thai approach - sit back, relax, and don't worry. You'll somehow eventually get there. And, in the meantime, you might find yourself in a fascinating part of the city you wouldn't have seen otherwise. Oh, and don't forget to tell the driver, "Mai Pen Rai", which means "don't worry, it's no problem".