The answer to that question, of course, is "it depends."
It depends on WHICH herbal remedy. It depends on what else you're taking. It depends on whether or not you take the herbal remedy instead of the effective medication your physician has prescribed. It also depends on who you ask. Sanjay Gupta, MD has an article on the TIME web site discussing some of the risks.
A few years ago, a young, healthy baseball player died after taking an herbal supplement containing ephedra to help him lose weight. Ephedra has since been banned by the FDA.
The research on Glucosamine and Chondroitin is less disturbing. It might actually be helpful in the treatment of osteoarthritis of the knee. If it keeps you from needing an NSAID, the risks are probably lower for Glucosamine with or without Chondroitin than for the NSAID as there are very few known side effects. Animal research suggests that it may impair glucose tolerance. I haven't found that to be an issue for me and I have cut way back on my NSAID use -- and I don't really care if this is some sort of placebo effect.
Kava is used to relieve stress or anxiety. It has been banned in several countries (but not the US, yet) because of potential liver toxicity. Any time someone selling a product tells you to use it only 3 days/week and 3 weeks/month, you've got to wonder how safe it is.
St. John's Wort may be helpful for treating mild to moderate depression, but it may interfere with a number of prescription medications such as antivirals for HIV, chemotherapy medications, and cyclosporine (anti-rejection medication for organ recipients). It definitely is not effective for major depression, bi-polar disorder, etc.
The most significant risk of herbal supplements is the risk that people might use them INSTEAD of effective medications. I had cancer several years ago. People I barely knew begged me to try various herbal supplements instead of the chemotherapy regimen recommended by my physicians. I did the research. The herbal supplements they recommended had been investigated by NIH and found to be useless. The chemo regimen had also been studied - in great detail - for many years and found to increase 5 year survival rates for cancer of the type and stage mine was from 55-65% with surgery alone to nearly 90% with chemo and radiation. Sort of a no-brainer there. It was hard for me to believe that people would not be convinced by the statistics, so I shared them with those who recommended herbs instead of chemo. They weren't impressed.
Some herbs are safe, some aren't. Some may help, some definitely won't. Do the research -- it's out there. Look for actual research (peer-reviewed studies) as opposed to pure opinion. Ask your physician. If he or she isn't familiar with the supplement, share your research. If you take prescription medications, make sure your doc knows what supplements you're taking -- and make sure your pharmacist knows too. It might save your life.