Cloth diaper covers have come a LONG way since plastic pants! You can choose PUL (laminated polyester fabric), fleece, or wool to provide waterproof covers for cloth diapers. All types provide more breathability than plastic pants. Using a breathable diaper cover keeps the temperature lower inside the diaper, which is more comfortable for the child and reduces diaper rash issues.

Each type of cloth diaper cover provides different benefits. PUL diaper covers are the trimmest and most commonly used option. Fleece and wool covers provide even more breathability, but with a little more bulk. Fleece and wool diaper covers require a little more care as well. Fleece covers usually need to be washed after each use. (PUL covers can often be wiped clean or hung up to air out between diaper changes.) Wool is naturally anti-bacterial, so can be air-dried and reused for several weeks between washings, but then it usually needs to be handwashed.

Many parents use fleece or wool covers over nighttime diapers.  They provide extra protection for heavy wetters, or for babies that sleep through the night (I've heard they exist...).  You do need to be careful not to tightly compress the fleece or wool cover, such as in car seat straps, or a soaked diaper will leak right through. 

Most cloth diaper covers come in different sizes - small, medium, & large.  A few are more adjustable, like the Blueberry CoverAll and the Thirsties Duo Wrap.  The benefits of the sized diaper covers are that they are simpler to use, and will usually last through multiple children, since you aren't using them for as long a period of time.  The adjustable covers are great for a baby that is hard to fit, such as extra long and thin, or extra chubby.  They also work well when a baby seems to be in between sizes.  If you use one of the one-size diaper covers to last the whole time your child is in diapers, you should plan on buying new covers for your next baby.  (One bonus is this frees you up to buy cutesy gender-specific diaper covers!) 

A pocket diaper or an all-in-one diaper will not need a separate diaper cover, as the waterproof layer is built-in.  But fitted diapers and prefold diapers will require a cover, or your child (and you!) will end up with wet clothes.