Some amoebae build elaborate houses for themselves to live in. (top and side view of an Arcellinid)
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)
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, arcella.nl -- pretty micrographs and lots of info on the lives of amoebae. Good for identification too. Truly a labour of love!