It can get very dense and plump but I can't seem to figure out what combo of light and water it needs to keep it that way. It gets baked by too much direct light and it has tendency to get really leggy if its in the shade. If I knew the name I could get some insight into its natural environment.
I agree that it looks like an Aloe of some sort. The whitish spotting on the leaves is a good indicator. Does resemble some ice plants though, if it blooms with outer-space looking daisys an inch wide its that. One thing about ANY succulent type plant though is that the root structures are going to want to breathe. Most succulents respirate through their roots and so even if you have just given one its thourough soaking (after having the soil dry out completely) the growing medium is going to want enough gravel, grit, sand, bark-whatever so that the roots will continue to get air at all times. Full sun for sure as well.