Definition : angiogenesis is defined as the growth of new blood vessels.

Angiogenesis, Cancer, and tumor growth
Tumors require oxygenation, nutrition and a route for dissemination. This necessitates the development of new vessels or angiogenesis. High levels of new vessel development are indicators of poor prognosis in cancer; they also provide new avenues of anti-tumor therapy. Angiogenesis in cancer produces structurally different vessels from angiogenesis in wound healing and inflammation. The importance of vascular endothelial growth factor (VEGF) as a regulator of normal and tumor blood vessel growth has been increasingly characterized over the past two decades. VEGF increases vascular permeability and has a well established role in stimulating angiogenesis, a prerequisite of tumor growth. Numerous compounds have been developed to counteract the angiogenic effects of VEGF.

Supplements that influence angiogenesis
There are several nutrients and herbs that influence angiogenesis in laboratory studies, whether these supplements would do the same when ingested orally by humans is not yet known, and how they interact clinically in terms of tumor shrinkage or growth is not clear at this time.

Ashwagandha is an Ayurvedic herb with antioxidant properties, you can see some research on angiogenesis on the web page provided as the link.

Bilberry anthocyanidins
   Inhibitory actions of bilberry anthocyanidins on angiogenesis. Phytother Res. 2010. Department of Biofunctional Evaluation, Molecular Pharmacology, Gifu Pharmaceutical University, Japan. The aim of this study was to examine the antiangiogenic properties and antioxidant activities of the main anthocyanidins (delphinidin, cyanidin and malvidin) found as constituents in Vaccinium myrtillus (bilberry) anthocyanosides (VMA) and of N-acetyl-L-cysteine (NAC). Each of these anthocyanidins concentration-dependently inhibited vascular endothelial growth factor (VEGF)-induced tube formation in a co-culture of human umbilical vein endothelial cells (HUVECs) and fibroblasts.

Cinnamon herb
   Biosci Biotechnol Biochem. 2015 Jan 3. Water extract of Cinnamomum cassia suppresses angiogenesis through inhibition of VEGF receptor 2 phosphorylation. Angiogenesis, the process of new blood vessel formation, has been a major target for cancer therapy. Antiangiogenic herbal medicines are useful in the treatment of cancer. In this study, we found that a water extract of Cinnamomum cassia (CCWE) was a potent inhibitor of angiogenesis. In cultured human umbilical vein endothelial cells, CCWE suppressed vascular endothelial growth factor (VEGF)-induced proliferation, migration, invasion, tube formation, and intracellular signaling events such as phosphorylation of ERK, p38 and VEGFR2, and activation of matrix metalloproteinase. Furthermore, CCWE inhibited VEGF-induced vessel sprouting of rat aorta ex vivo. These findings might be of particular interest for drug development because VEGF signaling is a potential target for treatment of angiogenesis-associated diseases.

Alpha lipoic acid plays an important role.
Genistein found in soy is available as a supplement'
Modified citrus pectin is of benefit
Reishi mushroom is popular in the Orient'
Resveratrol is found in grapes and wine
Silymarin found in milk thistle, and herb mostly known for liver protective effects;
Uncaria promotes angiogenesis

Angiogenesis in the brain
Angiogenesis is a crucial force for shaping the nervous system and protecting it from disease. Recent advances have improved our understanding of how the brain and other tissues grow new blood vessels under normal and pathological conditions. Angiogenesis factors, especially vascular endothelial growth factor, are now known to have roles in the birth of new neurons (neurogenesis), the prevention or mitigation of neuronal injury (neuroprotection), and the pathogenesis of stroke, Alzheimer's disease and motor neuron disease.

Alcohol, angiogenesis, and breast cancer
Moderate alcohol consumption stimulates the growth and progression of breast cancer by fueling the development of new blood vessels -- a process called angiogenesis. Alcohol increases angiogenesis by boosting expression of a key growth factor known as vascular endothelial growth factor or VEGF. Drinking alcohol -- even moderate amounts - is a well-established risk factor for breast cancer in women. A recent study found that 60 percent of breast cancer cases in women worldwide were attributable to alcohol consumption.

Angiogenesis inhibitor - inhibition
Inhibiting angiogenesis is a promising strategy for treatment of cancer and several other disorders, including age-related macular degeneration. Major progress towards a treatment has been achieved over the past few years, and the first anti angiogenic agents have been recently approved for use in several countries. Therapeutic angiogenesis (promoting new vessel growth to treat ischemic disorders) is an exciting frontier of cardiovascular medicine.

Copper mineral role
The formation of new blood vessels is the initial step in progressive tumor development and metastasis. The first stage in tumor angiogenesis is the activation of endothelial cells. Copper ions stimulate proliferation and migration of endothelial cells. Serum copper concentration increases as the cancer disease progresses and correlates with tumor incidence and burden. Copper ions also activate several proangiogenic factors, e.g., vascular endothelial growth factor, basic fibroblast growth factor, tumor necrosis factor alpha and interleukin. Whether attempts to reduce copper levels in a tumor microenvironment will alter cancer progression has not been fully evaluated.

Angiogenin
In addition to its well-known role in mediating angiogenesis, human angiogenin also directly stimulates prostate cancer cell proliferation.

Dr. Judah Folkman founder of angiogenesis cancer theory
Dr. Judah Folkman, a cancer researcher who discovered that tumor growth depends on the generation of a network of blood vessels that provide nourishment, a process called angiogenesis, died at the age of 74 in 2008.
He started an entire branch of cancer research called anti angiogenesis therapy. He believed that if the growth of blood vessels feeding the tumor could be stopped, the tumor would wither and die. This lead to the development of medications such as Avastin (Genentech) Avastin and other targeted cancer treatments.