Did The Greeks Combine Gods?

In Egyptian religion, there are times when Gods are combined, like Bast-Mut for example. Did the Greeks do anything similar?

Yes, from the Hellenistic period onward, cults of certain popular deities were routinely united and combined with each other.

Probably the most clear example is the cult of Diana/Ἄρτεμις. She came to be equated with several other deities, notably Trivia/Ἑκάτη, the Moon, Eileithyia (goddess of childbirth), with Themis, and most widely and popularly, with Fortune/Τύχη. 

Along with Vesta/Ἑστία, Ceres/Δημήτηρ, and Iuno/Ἥρα, she (and most other popular goddesses) was occasionally (especially by extension of her identification with the widely popular goddess Fortune) identified with Rhea/Cybele.

Apollo was largely merged with the Sun (Sol/Ἥλιος), and identified as well with the Anatolian Mithras. Pluto, Bacchus, Adonis, and Faunus (and other terrestrial gods of life and abundance) were often identified with one another, and with Graeco-Egyptian Serapis.