Some amoebae build elaborate houses for themselves to live in. (top and side view of an Arcellinid)

Some build their houses out of siliceous (glass) scales and peek out of them with thread-like pseudopods called filopodia. (optical sections of a Euglypha cristata from a soil sample)

Some amoebae can be naked. (Saccamoeba(?) Note the wrinkly-bulby uroid at its trailing end -- that's where extra membrane ends up after the amoeba moves)

And spiny. (Acanthamoeba)

Sometimes even eruptive. (a Heterolobosean amoeba from soil, with contractile vacuole in act of expelling fluids at the back)

And sometimes, a house-bearing amoeba can find itself enshrouded by squishy naked cytoplasm of doom. (Our Euglypha cristata inside a no-longer-hungry amoeba. Evidently, the spines didn't help. Don't know species of the murderous amoeba, but definitely an Amoebozoan ;-))

By the way, there is an incredible site on amoebae being developed as we speak by Ferry Siemensma, -- pretty micrographs and lots of info on the lives of amoebae. Good for identification too. Truly a labour of love!