We've done it, but it's expensive and was only worth it as we were renovating and plastering all our rooms anyway. Cost about an extra £400 per room in materials and labour on top the of the general plastering we were having done.
Our plasterer piled lots of rock wool insulation against the adjoining walls, then built a false plasterboard wall in front of it. We used Green Glue sealant along all the seams. He then plastered on top of it, we green glued all the edges and floor seam again before painting.
We also stuffed our loft space and the adjoining wall in the loft with more rock wool as sound travels up through walls and chimney breast.
Benefits:
about 50% reduction in noise so sounds like talking and music are reduced. We can generally hear the hum of them talking and laughing and make out some words, which is a huge improvement, but when they shout and argue and have their TV up really loudly (24/7 
) we still hear every word and the music on the TV over our own TV, so it wasn't quite as effective as hoped.
Cons:
we lost about 10cm depth from each room which didn't bother me.
You can't attach furniture/shelves/mirrors etc against the wall as it's drilling into plasterboard so can't be supported and also would allow sound to leak through the hole. This impacts on how you can use the space to place furniture.
we still hear and feel noise vibrations through the walls and floors as their TV is attached to the adjoining wall, or if the kids and dog are running around
It's amazing how much sound isn't through the walls, for example they always have their windows open as they smoke and the sound comes out of their house and in through our own windows
we made a mistake not blocking up the old gas fire flue and chimney breast which is where their TV is hung so the lounge and my daughter's bedroom above is still pretty noisy. If you have a chimney breast in your lounge I would strongly recomend you do this otherwise I think you'll be disappointed
Overall I couldn't have survived living in this house the past couple of years without the sound proofing so I'm glad we did it as it prevents our children hearing the details of the swearing/arguing. But it doesn't eliminate all noise in general.
If the TV is attached to the wall like so many people have now, you'd probably need to do the sound proofing in whatever room is directly above your lounge to get a cumulative effect. We did each room over about a year's period and the most noticable affect was when we finished the final room and completely sealed off all adjoining walls as sound travels
So it's not an easy or perfect solution I'm afraid and we're looking to move house next year to a detached property if we can stretch to it, never again will we live in a semi or terrace!!