Strength is often the most important reason for alloying, but there are several other properties that can also be tuned by alloying, such as : density, ductility, corrosion resistance, melting point, wear resistance, elastic modulus, machinability, thermal/electrical conductivity (and several others).
Wood's metal is a metal alloy that melts at an astonishingly low temprature, about 158 degrees Farenheit, it is an alloy of Bismuth, lead, tin, and cadmium.
Iron alloys like high carbon steel make them stronger.
Silicon alloys of Si and P along with Si and B are used together to make conventional solar panels.
Gold is alloyed with copper because copper is cheaper (less expensive).
Mechanical properties (strength, fracture toughness, hardness . . .) and corrosion resistance are the two main reasons that metals are alloyed. Interestingly, an alloy composition which is great for strength may not be great for corrosion, and vice versa.
I use ASM International's Metals Handbook, Desk Addition.
For detailed information, I'll go a particular standard from ASTM or SAE or other technical society responsible for that material. However, in many cases, the alloy properties are based on fully annealed material. Cold worked material will have greater strength and less ductility.
Also, if one looks at alloy composition, one will notice a range for the portions of principal alloying elements and usually an upper limit for 'impurities'. Mechanical properties, such as fracture toughness, and corrosion can vary significantly with composition variations, particularly when variations in thermomechanical schedules introduced. Thermophysical properties are less affected.