There is a pretty significant interest in DHEA on The Peak Testosterone Forum from what I have seen. One of our senior posters tried supplementing it with pregnenalone and felt it got rid of a lot of his mental fog.  Yet another poster wrote that DHEA restored his erectile strength:
"Since i was 18 i have suffered from cripling depression and anxiety along with constant stress. I started taking 50mgs of DHEA a few weeks ago and within a week or 2 i was getting morning erections for the first time in a long time, and achieving a solid erection." 
DHEA has had extensive research as a nootropic, anti-aging and nutraceutical compound. Furthermore, DHEA rapidly falls off with aging and low levels are correlated with many conditions - autoimmune disorders and heart disease in particular. There is also evidence that DHEA can battle depression and improve sleep.
And it has a couple of studies that show in some cases it can improve the modern plague of Metabolic Syndrome. It should be mentioned, though, that the studies have been mixed generally with DHEA and, once considered a wonder supplement, it has now taken a back seat to other approaches. Furthermore, I have never had a man write in and say, "Wow! Taking DHEA changed my life," which does happen quite often with TRT and thyroid hormones.
Regardless, I know that many men are interested in DHEA for the sole purpose of boosting their free testosterone when combined with HIIT (interval training). There is a well-known study out there - see my page on How to Increase Your Testosterone Naturally - for the journal citation. (See number 5.)
CAUTION: You have to be careful with raising your DHEA too high in my opinion. High DHEA can potentially cause neuron-related issues and some believe it could raise estradiol in some men (although I have not seen good evidence that this is the case). In addition, Ray Sahelian has reported some arrhythmia side effects at higher dosages. Work with your doctor or naturopath and find his or her experience.
So can DHEA be increased naturally? Here are some of the herbal and supplemental solutions that may increase DHEA in some men. Now are these any safer long term than just taking DHEA? Well, your guess is as good as mine. There are some physicians who prescribe DHEA and so they might have a feel for safety in the short and medium term.
1. Tongkat Ali. One recent study showed that Tongkat Ali can increase DHEA, at least in some men.  It also normalized testosterone levels in many men, but keep in mind that the study had a high dropout rate for reasons unknown and it consisted of only hypogonadal males.  Anecdotally, we had one senior poster say that it did nothing for one of his friends, so the formulation and dosage may be important.  It has the additional benefit of possibly lowering cortisol as well. 
2. Tribulis Terristris. Animal studies - specifically on primates - have shown that tribulis terristris increases DHEA levels.  This may very well translate over to us as well, since we're all one big, happy family.
3. Magnesium. There is a lot of talk around the web - but not studies to back it up - that magnesium can increase DHEA levels. The anecdotal evidence seems to be that it works for some men but not for others. According to Jack Ruse, this may depend on inflammation. 
If you'll notice, the research backing herbal and supplemental approaches to raising DHEA is spotty at best. Again, you can take a DHEA read before and after trying one of the above - I'd get it approved through your doc if you have a medical condition or are on any medications - and then see if there is any change. By the way, this can be done quite inexpensively through one of these labs: Testosterone Labs. (I have no affiliation with any of them.)
So what about simply taking DHEA directly instead? Of course, this is quite common and there are essentially two ways to do that:
1. Oral DHEA. This has a short half life (less than 30 minutes) and is probably best taken twice per day to try to compensate. DHEA is also fat soluble and thus should be consumed in a meal with some fat in it.
2. Transdermal DHEA. DHEA can also be applied topically, much like testosterone. One study showed that it was absorbable in men and increased plasma levels as expected.  I have read that Dr. Crisler, one of the very well known "internet HRT docs" believes that transdermal DHEA is the most effect form. And Dr. Mercola is also a big transdermal DHEA fan with a twist: he believes it should be applied rectally. I'm not sure how practical the latter is on a daily basis. You have to make sure your compounder knows what he/she is doing if you try this approach as a harsh delivery system could leave you standing for a couple of days!
4. Vitamin C. One older study showed that 4 grams of Vitamin C per day lowered the solid majority's of men's cortisol and simultaneously raised DHEA.  In fact, the DHEA increase (after 1 week) was rather profound from 426 ng/dl to 755 ng/dl, a 77% increase.  This was on young, healthy volunteers, making the results even more provocative.
1) Andrologia, 2012 May;44 Suppl, "Standardised water-soluble extract of Eurycoma longifolia, Tongkat ali, as testosterone booster for managing men with late-onset hypogonadism?"
3) http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3669033/, ""Effect of Tongkat Ali on stress hormones and psychological mood state in moderately stressed subjects"
6) Phytomedicine, 2008 Jan, 15(1-2):44-54, "The hormonal effects of Tribulus terrestris and its role in the management of male erectile dysfunction--an evaluation using primates, rabbit and rat.
9) Physiol Res. 2000;49(6):685-93, "Effects of transdermal application of DHEA on the levels of steroids, gonadotropins and lipids in men"
11) Annals NY Acad of Sciences, Jul 1987, 498:487 490, "Bimodal Effects of Megadose Vitamin C on Adrenal Steroid Production in Man"