1. When you're traveling loose with no real agenda.
When you are traveling in an open-ended and open-minded way, my feeling is that hiring a tour guide can remove opportunities for spontaneity and chance or luck (both good and bad, of course). If you want to hang loose, do it -- you don't need to hire anyone to help you.
2. When revisiting after having already used a guide.
When you return to ground you have already covered with a guide, it seems time to venture out on your own to find your own hidden treasures, rather than having someone show you a map.
3. When traveling solo.
Traveling alone gives you plenty of opportunities to interact with locals, and allows you to improvise to an extent that hiring a guide might only hinder the strange and (hopefully) wondrous things that might come your way.
4. When you have a lot of activities planned.
If you're already heavily scheduled, avoid adding to your sightseeing obligation by hiring someone to help you pack in even more stuff.
5. When you do not want to be on a schedule.
Sometimes travel isn't about sightseeing or investigating history -- sometimes it is purely a time to unwind. If this is the case, having a guide who will roust you from the balcony of your hotel room and force you to get dressed and go "experience" things is simply counterproductive.
6. When in a very small place.
Let's face it, you don't need a guide to take you around a place like Whidbey Island in Washington; you need a bike.
7. When you want quiet time to yourself.
More than just pointing the way around a place, a good tour guide engages his or her clients on many levels -- with conversation, storytelling and humor. If you are feeling antisocial or just want to be left alone for a few days, hiring an enthusiastic tour guide is probably not your best option.
8. When you want to practice a language.
If you want to challenge your language skills with complete immersion, hiring a guide who speaks your language can create a buffer that will undermine any attempt to see if you make the grade in a foreign language. If immersion in the language and culture is your goal, force yourself to operate and communicate without the safety net of a (paid) native speaker at your side. (One caveat here: Practicing a language one-on-one with a dedicated tour guide who is willing to speak to you entirely in his or her native language may be better -- and more affordable -- than a language school.)
The Independent Traveler