The short answer is: in most cases, yes. There are psychological benefits to getting a massage; mainly relaxation and peaceful frame of mind. Some of this can be attributed to the physical benefits outlined below. There is also the simple act of releasing tension and allowing the body and mind to “let go,” relax and breathe. For the bulk of this post, however, I will focus on the main physical effects.
Please also read to the end, where I outline reasons regular massage might NOT be healthy.
Since the muscles constitute one half of the bulk of the body, and receive one fourth of all the body’s blood supply, any procedure which acts directly on the muscles has a decided influence on the whole body. When done properly, massage (specifically flushing techniques such as friction and manual lymphatic drainage) refreshes the supply of oxygenated blood to the tissues it acts upon. Painful chemicals are also cleared (such as bradykinin, histamine and substance P, lactic acid, eicosanoids, nitric oxide, adenosine, cytokines, and others ). This reduces pain by removing its cause(s), and increases comfort and proper function (including strength and endurance) through relaxation of and better circulation within the muscular fibers.
Skeletal and ligamentous
Massage can also influence such harder structures as bones and ligaments (the connective tissue attaching bone to bone). Bones have essentially the same blood supply as their overlying muscles, and the flow of the blood vessels and lymphatics is largest in the vicinity of the joints. When muscles or joints are engaged, the movement of the fluids increases the nutrition to these areas which furthers their growth. 
General massage increases the rate and force of the heart beat differently than exercise. Massage does not raise arterial tension or stimulate the neuromuscular junction as does exercise, and while massage produces a full, strong pulse, it does not accelerate the heart to the same degree. Massage mainly affects peripheral circulation. Rubbing techniques (friction) act mainly on superficial veins while deep tissue and rolfing techniques, etc., act on deeper vessels also.
Lymphatic vessels are aided in the flushing of waste and toxins from the body by friction and kneading techniques, because they are most abundant in subcutaneous tissue and in the fascia which coat and lie in between muscles. 
As with exercise, massage increases the depth of respiratory movements. Partly, this is due to the parasympathetic reflexive influence of massage. But massage also helps in bringing certain circulatory waste products to their elimination point in the lungs. Massage increases oxidation, or CO2 production, by the heat and increased metabolism it creates in the muscles. This then improves oxygen absorption in the tissues, and CO2 elimination through the venous blood. 
Many specific applications of massage therapy are used to achieve specific physiological goals. These include manual lymphatic drainage to reduce local swelling; deep tissue massage, Active Release, Thai massage or Rolfing to break up fascial / tendinous adhesions; trigger point therapy or myofascial release to address specific types of tension within specific muscles or myotatic groups. Each technique has its functional directives. Many different disciplines of medicine utilize massage / manual therapeutic techniques to achieve certain goals. These get more specific with advanced techniques.
Reasons Why Regular Massage Might NOT Be Healthy
There are several contraindications (reasons why a technique is inadvisable and possibly harmful) to massage:
Significant fever: The body is already under siege from infection or inflammation; massage will only increase the problem, not help.
Uncontrolled infection: The body is already overloaded trying to attack the invading / inflaming organism. Massage will only add an additional overload and complication, most likely making symptoms worse. Wait until the infection is identified and eradicated before having a massage.
Recent severe injury or surgery: There are advanced techniques such as manual lymphatic drainage and craniosacral therapy that can help control initial swelling and inflammation, but general massage would overload the body’s capacity to respond favorably in such a compromised state.
There are also many fields of specialization within manual massage therapy. Some good recent research (although more is needed) includes:
https://www.researchgate.net/publ… Physiological and clinical changes after therapeutic massage of the neck and shoulders.
https://www.ncbi.nlm.nih.gov/pmc/… Preterm Infants Show Reduced Stress Behaviors and Activity after 5 days of Massage Therapy
https://www.seminarsoncologynursi… Massage in Supportive Cancer Care
https://www.ncbi.nlm.nih.gov/pubm… Effects of patterns of pressure application on resting electromyography during massage.