Few things are morning important to your penile health than those morning erections. Why? Oxygenation. Oxygenation. Oxygenation.
I get emails all the time from men that have lost their morning erections for months or even years. This is a tragic situation, because morning erections, through oxygenation, help maintain healthy erectile tissues. Without that oxygenation, researchers have noted that "fibrosis" sets in, which means a hardening and aging of the structures. 
This is why I insist that men, if they no longer have morning erections, must somehow, someway make sure they get several erections during the day. By the way, this is one of the reasons that sex is so good for males: it literally helps to maintain their sex life. "Use it or lose it" as they say.
NOTE: Morning erections, or the lack thereof, can be a good way to begin troubleshooting if you have psychological (or psychogenic) erectile dysfunction. The idea is that if you can achieve an erection by any means, nightime or otherwise, then your issue is probably not physical (organic). In fact, this has been used by diagnosticians for literally decades as an starting point tool.  In fact, one study noted that "the single best predictor was the presence or absence of early morning erections as reported by the patient."  (Now my opinion, and I cannot back this up with a study, is that this might be confounded by depression and other mood disorders. Perhaps depression can suppress morning erections before an underlying testosterone or nitric oxide issue has developed.)
So what causes morning erections? They seem quite mysterious in many ways and even "automatic" and "random" at times, i.e. they occur even without an erotic or sexual dream involved. However, researchers have noted many lines of evidence and studies that show morning erections are primarily androgen-dependent, i.e. they are regulated by testosterone and DHT. 
In My Book on Testosterone I point out that several studies have shown that when testosterone falls far enough, you are likely going to lose and/or greatly diminish the number of your morning erections. That doesn't necessarily mean that you won't still be able to "get it up" during the day, however. The reason is that a normal erection is achieved through a different pathway involving the senses of touch, sound and sight. However, if you allow your testosterone to remain at low enough levels for a long enough period of time, you are opening the door to Venous Leakage and other erectile difficulties.
CAUTION: Some men think that DHT (dihydrotesteosterone) doesn't really matter and just causes hair loss. However, DHT is an incredibly important androgen and has been shown to be partially responsible for morning erections.  Before you take any DHT-blocker, be it Saw Palmetto or a drug, read this link on Propecia Risks.
Morning erections are not just dependent on DHT and testosterone, however, and the evidence points to the critical role of nitric oxide as well. Nitric oxide within the corpus cavernosum, the "erection cavity" within the penis is what dilates the penile arteries and causes the morning erections.
And that leads to this important question:
"What can one do to get his morning erections back?"
Below we give you few ideas:
1. Testosterone. This may seem obvious, but many men don't make the connection: you have got to have adequate testosterone levels in order to fire off those morning erections during REM sleep. One's "morning wood" is really linked to a different system than standard waking erections and requires adequate testosterone as a sort of fuel. For example, one study showed that when levels fall below about 200 ng/dl, men can expect issues. 
Further verification comes from the fact that several studies show that testosterone therapy (Hormone Replacement Therapy or HRT) steadily restores nocturnal erections in men with low testosterone. In fact, one interesting study took a bunch of hypogonadal men and gave them a hefty shot of testosterone cypionate. They then monitored the men over the coming weeks during sleep and watched the morning erections spike and then slowly decrease to about half the frequency. . The researchers (somewhat cruelly) let the men's testosterone levels shrink to almost nothing and by the end of 8 weeks, the men's rigidity had gone from 770 to 590 g, a loss of almost 25%! Yes, these men lost their superpowers and their nocturnal erections at the same time.
Of course, there one doesn't necessarily have to go on HRT (TRT) if you find that you are low testosterone and lacking in morning erections. Check out my pages on Common Causes of Low Testosterone and How to Increase Your Testosterone Naturally for more information.
NOTE: It can take time for the restorative process. One study noted a year of continuous improvement in REM-related erections.  Read this link on Venous Leakage to understand how testosterone helps erections via two primary pathways: 1) increasing eNOS (the "nitric oxide enzyme) activity and 2) restoring the internal structures and tissues of the penis.
2. Nitric Oxide. Many men notice that when they begin to take one of the PDE5 Inhibitors (Viagra, Cialis or Levitra), their morning erections improve. I have also received letters from many men who have noticed the same thing after taking various Erectile Supplements - maybe even an Erectile Supplement Cocktail - or increasing their exercise. The reason, of course, is that all of these usually increase arterial nitric oxide levels, including those in the penis, and this will in turn help with morning erections.
In fact, improving nitric oxide can have dramatic effects on nocturnal erections as one Cialis study showed. Cialis has a long half life and its efficacy is considered to be about 36 hours in most men. One study showed that men who used 20 mg every other day had dramatically increased morning erections.  The authors commented that "chronic treatment also produces a dramatic increase in morning erections, which determines better oxygenation to the penis, thus providing a rationale for vascular rehabilitation." (The PDE5 Inhibitors like Cialis also have a long list of side effects, some very serious. We have had men on the Peak Testosteorne Forum with long term and probably irreversible hearing and vision damage.)
A Viagra study using 100 mg nightly for three nights showed some impressive results as well on men with erectile dysfunction.  The primary change seen in the case of this PDE Inhibitor were prolonged morning (nocturnal) erections - in fact, about 60% longer.
Am I advocating taking PDE5 Inhibitors in order to get your morning erections back? That, of course, is between you and your doctor, but every attempt should be made to take only the minimal dose necessary and ideally for only the short term. Remember, one can also experience PDE5 Inhibitor Resistance and PDE5 Inhibitor Dependency, so you want to be careful with these medications. Finally, it is important to rely as much as possible on Exercise, Erectile Foods, gradual Weight Loss and Sleep to boost your nitric oxide and restore you endothelium.
3. Sleep. The importance of sleep to morning erections is often ignored. Nocturnal erections occur during REM sleep and some men with erectile struggles report that they seem to be able to achieve nocturnal erections if they sleep long and thus get that last all-important REM cycle.
4. Sitting. One reader has a novel approach, where he sat slightly erect, and found that his morning erections re-commenced. See this link on A Novel Approach to Morning Erections for an example.
5. Pycnogenol. Studies of Prelox, which is just Pycnogenol with a low dose of L-Arginine, show an increase in morning erections.  Of course, Pycnogenol is known for improving erectile dysfunction, increase nitric oxide and decreasing inflammation. See my links on Pycnogenol and Erectile Strength and The Pros and Cons of Arginine for more information.
6. Stress. Anecdotally, men have reported to me increased morning erections after taking any of the cortisol reducers (Vitamin C, S-PS, etc.) As you know, if you have been looking around the site, I frequently recommend regular (non-religious) medititation and/or Progressive Muscle Relaxation for the same reason.
1) The Journal of Sexual Medicine, Nov 2005, 2(6):771ï¿½784, "Testosterone and Sleep-Related Erections: An Overview"
2) The Journal of Clinical Endocrinology & Metabolism, Apr 1 2002, 87(4):1467-1472, "The Effects of Transdermal Dihydrotestosterone in the Aging Male: A Prospective, Randomized, Double Blind Study"
3) Journal of Sex & Marital Therapy, 1983, 9(1), "Serum testosterone and prolactin levels in erectile dysfunction"
4) Journal of Sex & Marital Therapy, 1975, 1(4), "The assessment of nocturnal REM erection in the differential diagnosis of sexual impotence"
5) ARCHIVES OF SEXUAL BEHAVIOR, 1987, 16(2):125-137, "Use of sexual history to differentiate organic from psychogenic impotence"
6) International Journal of Impotence Research, 2007, 19:200ï¿½207, "Relationship between chronic tadalafil administration and improvement of endothelial function in men with erectile dysfunction: a pilot study"
7) Journal of Andrology, 18(5):522-527, "Relationship between sleep-related erections and testosterone levels in men"
8) Journal of Andrology, 13(4):297-304, "A long-term, prospective study of the physiologic and behavioral effects of hormone replacement in untreated hypogonadal men"
9) Phytotherapy Research, Mar 2009, 23(3):297-302, "Improvement of seminal parameters with Preloxï¿½: a randomized, double-blind, placebo-controlled, cross-over trial"
9) The Journal of Clinical Endocrinology & Metabolism, Mar 1 1990, 70(3):792-797, "Testosterone Replacement Therapy and Sleep-Related Erections in Hypogonadal Men"
10) Urology, Dec 2000, 56(6):906-911, "Sildenafil taken at bedtime significantly increases nocturnal erections: results of a placebo-controlled study"