Yeah, there's dumbbell exercises for a lot of things, as long as you have dumbbells heavy enough. For example, you could even do a 3day split with just dumbbells.
monday - legs
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goblet squats/dumbbell squats
dumbbell stiff-leg deadlift
calf raises (on raised edge)
wednesday - back+biceps
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dumbbell deadlifts
dumbbell rows
dumbbell pullovers
curls
friday - chest+shoulders
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incline dumbbell press
flat dumbbell press
db shoulder press
db skullcrushers
see..
obviously it'd be better if you had barbells, a pullup bar and a few machines (for pulldowns, calf raises et al). And you also need DB's heavy enough, which will be quite heavy eventually if you get pretty strong.
Any reason you can't get a barbell and some plates (and a power/squat rack), or join a gym?
-shaun