Pros:
Cheaper in the long run - I've spent maybe £200 on nappies (not including the ones I've sold on) compared to I think it's £3000 estimated on disposables? My nappies will be used on hypothetical baby 2 as well
Cost per wear for brand new mainstrem reusables (the types available in supermarkets/Boots) is about 4p in cluding the washing. The cheapest disposables I've seen are 7p each.
You don't have to drag a screaming baby round a supermarket to buy them
You empty the bin at your leisure, not the council's, meaning you don't have to put up with the stink unless you choose to
The resources used to produce and wash a cloth nappy are still far far fewer than those needed to produce the equivalent amount of disposables
They can be used as an item of clothing in their own right. I use wool covers most of the time for ds and his nappy cover and trousers/shorts are the same thing. Wool only needs washing every 4-6 weeks (urine+lanolin=soap so they're self cleaning to a certain extent) which has massively reduced my regular laundry load, even though I'm still washing nappies - I'd be doing that anyway!
Disposable nappies smell of chemicals. This is something that isn't noticeable until you're used to having your child in cloth then go back to sposies for whatever reason. Pampers honk!
Cons:
You have to be organised and wash them
You have to find somewhere to store them
You have to have space to dry them
People ask questions about them All The Time, but woe betide you for answering with enthusiasm or they might think you're criticising their choice on here anyway. In real life people are just polite IME
Your mother and mother in law will be HORRIFIED. Until you show them how pretty and easy modern ones are, anyway 
It's very easy to fall into the trap of buying a large amount of one type in a special offer bundle, finding they don't fit your baby, and deciding Cloth Nappies Don't Work. Best thing to do is buy one or two of several types - lots of councils have trial schemes, or find a local nappy library - then stock up once you know what works on your baby. Nappies are like jeans, the brand that's amazing on your best mate will probably look hideous on you!
DS has been in pretty much full time cloth since he was 5 days old. Different brands and types of nappy have worked for us at different stages, and I've bought nearly all of them second hand - and sold a fair few on once we didn't need them any more too. I've done a rather long post here, feel free to ask any more questions though 