Most of non-flagellated cells often follow the amoeboid movement. Ex. Macrophages
Euglenoid movement
Euglena is another single cell eukaryotic organism. Euglena contains flagella as well as pellicular structure. Euglena can move by waving the flagella. Pellicular structure of the euglena also help them to move. Adjacent pellicular strips move very quickly thus by changing own shape euglena can move without the help of flagella.

Paramesium (ciliary) movement
Paramesium is one more single cell eukaryotic organism which show cilia movement. Dense hair like cilia is present on entire outer surface of the euglena. In a coordinated manner, cilia move one after one all over the body result the paramecium movement.

Movements in animal cells
Animals, insects, birds, reptiles and fishes are multicellular eukaryotes. They migrate in three different modes. They are amoeboid movement, ciliary movement and muscular movement.
Amoeboid movement: In animal cell migration is possible by cytoplasm streaming which followed by the formation of pseudopodia. In animal cells, microfilament involvement is observed in amoeboid movement.
Ciliary movements: Cilia is the short form of the flagella present in ciliated epithelium. Coordinated movements of cilia helping those cells to migrate. The function of cilia almost similar to flagellum.
Muscular movement: In higher organisms, muscles based movement is very common. Coordinated function of muscles, skeletal and neural systems results the muscle movement.

Locomotion in lower animals
In lower animals skeletal system is underdeveloped or absent. In such condition they have to use muscles or specialized locomotive organs for the locomotion. Ex. Earthworms, snails, snake, fishes, etc.

Locomotion in Earthworm:

Long tube like structured earthworm moves underground by means of waves of muscular contraction. During muscular contraction body segments are alternatively shorten and lengthen. A special type S-shaped setae ring present in all segments of the earthwork except first, last and clitellum which help to anchor the surrounding soil. Mucus lubrication secretion make easier of their movement in soil.