Select is a good option here. Jason has shown in the comments how to use the Positive function. If you want a bit more flexibility for future usage, you can use a standard greater than operator.

data = {{-1, 0}, {0.2, 0.4}, {4, 0}, {0.3, 0}, {0.2, -0.4}};    
positive data=Select[data, #[[2]] > 0 &]

Select is a good option here. Jason has shown in the comments how to use the Positive function. If you want a bit more flexibility for future usage, you can use a standard greater than operator.

data = {{-1, 0}, {0.2, 0.4}, {4, 0}, {0.3, 0}, {0.2, -0.4}};    
positivedata=Select[data, #[[2]] > 0 &]