I was running a 2 x 9 setup on my daughter's bike with 36 and 24 front chainrings and a 7 speed 14-28 tooth rear cassette.
Getting a new rear wheel meant that I could run a 9 speed rear cassette. With an 11-34 tooth gear range it soon because apparent that by going to a single 28 tooth front chainring the gear range would be the same as the 36/24 14-28 range of the previous chainring/cassette combination.
What are the advantages of 1 x 9?
The key advantage is you can do away with having a front shifter, front derailleur and associated cabling. You also do away with a front chainring as well.
You do however need a few extras - without a front derailleur the chain can easily jump off the front chain ring. A chain keeper / guard is needed. Here's a picture of a prototype that I made. It works well. You'll have to excuse the dirty great bolt holding the clamp on, its was just temporary to make sure the concept worked. The picture also shows a 24t granny ring, but the chain keeper profile it optimised for a 28t chain ring.
Here's the final chain keeper (bashring also shown):
A bash ring is also a good idea. It will stop the chain derailling to the outside and also it provides a little added safety by protecting young calves from chain ring 'bite'. I couldn't find a suitable bash ring (30t size just big enough to cover the 110mm spider on the Sugino cranks ) so I custom made one for a perfect fit .
How much weight can I lose going to 1x9?
Along with the reduced complexity comes a reduction in weight by going to 1x9. I was able to ditch an XT front shifter pod (120g), a LX front derailleur (145g), 36t middle ring (55g) and some shifter cable and housing (maybe 20g). Total weight of stuff removed - 340g.
But, there was some stuff we needed to add back on: 30t bash ring (30g) and chain keeper (32g).
So total weight saving was around 278g.
Wider range cassette?
There are no real off-the-shelf options.
You can get a speed Shimano CS-HG61 Cassette (9-Speed, 12/36T) cassette, but its heavy at almost 500g. You can also get a Sunrace CSM99 11-36T cassette which may be lighter, but there's very little information available on this cassette.
The final option is to build your own by combining several different cassettes and an extended range cog. By combining an 11-34T XTR, 12-34T XTR and e*thirteen EX range 40t extender cog, I managed to put together a 12-40t cassette that has a great spread of gears but also a very even spacing.