The Equal house system was used in acient India and by Ptolemy.  Today we find it used in Britian, as it was promoted by Carter, Hone, the Faculty of Astrological Studies and The Mayo School of Astrology.  Each house is, of course, exactly 30 degrees, and it is therefore the easiest system to construct.  The equal house system supposedly reveals the essential spirit, soul, and personality of an individual.  It can be argued that this system is unscientific since the house cusps are based solely on time; the place of birth is irrelevant.  Fred Gettings (Dictionary of Astrology) states that the equal house system "is of exceedingly dubious value".Except in rare occasions, the MC / IC axis does not coincide with the 10th / 4th cusps. 

Porphyry (c. 300 A.D.)contended that the four Angles should correspond to the house cusps:  ASC=1,  DSC=7, MC=9, IC=4.  A rough and antiquated system which is no longer used today. 

The Campanus system -  revealing in psychological orientated work. 
Campanus lived in the 12th Century. 

The 8th Century Arabian astrologer ben Djabir derived the system that Placidus di Tito supposedly invented in the 17th Century.  It became widely used because of its ease of printing it in table form.  Raphael published it in 1821, and many subsequent ephemerides included these table. It remains popular to this day, probably due to its availability rather than any inherent advantageous characteristics. 

Regiomontanus  -  this is used primarily in hoary work. 

Meridian  -  evidently this is the favoured house system for Uranian astrology (is this advocated by the Hamburg school?).  One advantage is that it does not become distorted at high or low latitudes eg. for births in Scandinavia, Alaska, Singapore or Quito.  The first house cusp does not necessarily coincide with the Ascendent. 

Topocentric  -  this system relates directly to the natal latitude rather than to divisions of time.  It was first published in 1961 by Polich and Page of Buenos Aires.  British astrologers Kemp and Cornelius stated that this is the most precise house system, but the cusps are nearly identical to the Placidus system.  Tables are available for any latitude, 0 to 90 degrees. 

Koch  -  widely used in Germany, where it was devised in 1962, and other European countries.  Apparently gaining popularity elsewhere.  Not valid for high latitudes.  Especially useful for timing of events.