First off, why do I cloth diaper? It's three-fold:
1. earth-friendly
2. budget-friendly
3. baby-friendly
I really couldn't say about which of these reasons I feel more strongly, I'm equally passionate about each I suppose. I really do like the idea of soft fluffy cotton up against my babe's bum though. But anyways... Here are my favorite products:
Hands-down these Green Mountain prefolds are the best prefold out there. I have about two-dozen of the newborn (orange-edge) and small (yellow), and a dozen-and-a-half of the red, brown and green-edge each (Kolbe is currently in the brown-edge at almost 9 months with plenty of room to spare). I also have a handful of their premie-size prefolds, which work great for doublers, especially when they are teeny-tiny. I fasten the prefolds with a snappi, which is super cool and way easier than pins.
The red-edge medium size prefolds also work great to embellish/use as burp-cloths.
I also have a handful of homemade fitteds that are nice, especially for on the go. Read more about how I made them here (or click on the "cloth diapers" label to see more posts about these). 
I made this one (a large, which Kolbe is just now starting to fit) fleece-lined for a softer, drier feel.
I have tried several covers including Bummis Super-Whisper (not a huge fan) Bummis Super-Brite, which I like okay, they work best for a slender baby/toddler (in my opinion), but my favorite is definitely Thirsties or Thirsties Duo. Kolbe is currently in the Duo size 2 with all the snaps undone. The size large in the regular Thirsties is just a bit bigger than the size 2 duo (and still too big for Kolbe by quite a bit), and the mediums in the regular Thirsties are a bit snug on him now but work in a pinch. I like to have 4 or so covers on-hand in any given size, and they wear well. I typically use the same cover all day. Or you can rotate covers between diaper changes. Here are some pics of the children in various covers. Gemma and Kolbe in large and small Bummis Super Brites.
Gemma at 8 months in Thirsties medium. 
Kolbe at four months (stripes) and eight-and-a-half months (orange) in Thirsties Duo size 2. 
I also have a handful of smaller, homemade (by some friends) wool shorties and longies which I used on occasion with Kolbe. Wool is very absorbent/waterproof, it just takes a little more care. But it is oh-so sweet looking.
Now on to nighttime diapering! I used disposables at night for Gemma (who switched to cloth around 7 months), but really wanted to figure out a nighttime cloth solution for Kolbe. And after trying a handful of things, I have found something that works (at least for now). I have about a half-dozen bumGenius 3.0 size larges (which have fit him since he was 4 or so months). These already have a bit of built-in absorbency. I stuff them with a BG stay-dry doubler and then use one of these inserts from Green Mountain. Scroll down towards the bottom and find the one that is an hourglass shape (night stay-dry doubler). These are amazing. This diaper is usually on him for around 12 hours (no, he doesn't sleep that long, but I like to avoid middle-of-the-night diaper changes if I can), and the polar fleece on the doubler keeps his little bum nice and dry. It is honestly not even red in the mornings. And no leaks!! Seriously. I switched Gemma to the bumGenius towards the end of her night-diapering career (she's in underpants now) and that seemed to work well. I like these diapers a lot. I think the aplix (velcro) is going to need some attention after the fairly heavy use they get, but I'm sure I'll figure something out (they make repair kits you can purchase for around $1).EDIT: I switched Kolbe to disposables at night when he was around nine months. I use Earth's Best and they seem to do a very good job overnight.
Gemma (2.5 yrs) and Kolbe (7 months) in their bumGenius night dipes. They are both size large (Gemma's is actually a one-size, but it is the same size as the large at its biggest).
Some great (but not absolutely necessary) accessories to have on-hand for cloth diapering are wet-bags, a diaper sprayer, a diaper pail (okay, this one is necessary) and some wash-cloths to use as wipes. I have a handful of these cheap ones from Target, and also some of these homemade flannel wipes. I just get the wipes wet at the sink before a diaper change and then toss them in the pail along with the diaper. They seem to work great.
It is also nice to have some sort of non-chemical spray with which to spray your diaper pail between launderings. I like this product from BioKleen, and get it in the natural section at the grocery store. I use this for other various uses around the house as well, and even add a bit to my diaper laundering on occasion. There are so many different approaches to laundering (just like there are multiple approaches to cloth diapering in general) so again, here's what works for me. I launder every 2-3 days, and just keep the wet/dirty diapers in the dry pail in Kolbe's closet in the meantime. See below for directions on rinsing the poopy ones, I don't rinse the potty ones. They do fine and the smell really isn't bad. My laundry routine goes like this:
1. Dump diapers in washer and run one short wash/rinse on cold/cold (this rinses away most of the gunk and funk).
2. Do a long wash/rinse on hot/cold using a small amount of detergent. (I use Arm and Hammer Free and Clear powder and only use about half-way up to the "1" line on the scoop. You don't need much. Detergent residue contributes greatly to stink, especially from potty. Anyways, the big deal with detergents is to chose one that is natural/free of dyes, perfumes, whiteners, brighteners, etc. There are tons out there from which to choose, you just have to find what works for you and your babe.) I digress.
EDIT, I have switched to Rockin' Green Detergent (as of Nov. 2011) and LOVE it! You can order it directly from them or from various cloth diapering websites. I have started using it for most all of my laundry and been very happy with it. They make versions for soft and hard water as well.
3. Do a short wash/rinse on warm/cold to rinse away the rest of the detergent and that should be good. I always double check that the suds are essentially gone on the last rinse. If not just do another rinse.
4. I go back and forth between using the dryer and drying on my collapsible drying rack. If it's sunny and warm and not terribly windy, I love drying outdoors. The sun does wonders for stains and smells! If I dry in the dryer, I NEVER put my covers or bumGenius in. The covers air-dry very quickly, and the dryer is hard on them and will shorten their life considerably (learned this one from experience). I store my diapers in a laundry basket under the changing table, so they are contained and just an arm's reach away, plus I have several other baskets on the shelf of the changing table where I keep covers, doublers, etc. It's handy.
If you breastfeed exclusively, poopy diapers can be thrown directly into the diaper pail and into the wash from there with no additional rinsing. Formula-fed poopy-diapers and ones after your baby starts solids need to be rinsed (the diaper sprayer comes in handy for this) before washing.
My favorite cloth diapering website is Cotton Babies (great selection and free FAST shipping no matter how big or small your order, plus they are really nice and their customer service is fabulous), but I really like Green Mountain as well (and that's the only place you can get the Green Mountain prefolds), you just pay a little more for shipping (around $7/order I believe).
So there you have it! As I said, this is what works for me. Everyone has different preferences and ways of doing things, but I know I learned a lot (and still do) just talking to others and seeing how they did things, what they use, etc. I hope this can help you out! Cloth-diapering is wonderful. It's good for your baby, your pocket-book and the environment; and quite honestly it is just fun. If you have any inkling at all to give it a try I would highly recommend it, I promise you won't regret it!
And if you already cloth-diaper, please share some of your tips and tricks in the comments. I always enjoy reading about others' methods as well!!
