The ‘Notte dei Musei‘ was a great success in Rome and said success sees the idea carried over into the Summer, with most State Museums staying open late on Saturday nights (8 in the evening until 1 in the morning).
‘Estate nei Musei’ runs from June 25th until September 30th 2011; information (in English) is a bit scrappy and a bit scattered, but a look here and here will give you something to go on. Alongside museum openings there are also a whole series of parallel events and activities planned.