Seatposts need to be lubricated where they go in the frame, and also need to be removed and re-lubricated annually. Without this, the seatpost can sieze in place, requiring a saw and labor to remove it.
From http://www.yellowjersey.org/stukmk1.jpg and http://www.yellowjersey.org/stukmk2.jpg as of 2012/06. This is a post which was on the way to siezing but had not yet fully siezed.
Seatposts sieze this way due to a combination of design choices.
Seatposts are clamped at the top of the seat tube, but are not clamped at the bottom. In normal use, they wiggle around slightly down inside the frame.
The wiggling gradually wears the seatpost and frame. The wear is microscopic, so will not wear out the frame or seatposts, but it keeps rubbing off the surface material on the post and frame.
The fresh surface oxidizes — reacts with oxygen in the air. Metal oxides are slightly larger than the original metal. (See, for example, FAIL-102.) A seatpost is originally made loose enough to slide in and out, but once oxidized it is so tight it becomes permanently stuck and typically must be destroyed to be removed.
Quill-style stems have the same problem: the stem is held at the bottom and can wiggle at the top. They also sieze in place if not lubricated periodically. Ahead-style stems do not typically have this problem, though some "art" designs may.
The usual solution to the seatpost siezing problem is to simply remove the seatpost annually and lubricate it. Lubrication reduces wear and slows oxygen intrusion. However, enough lubricant is pressed out over time that the post will sieze if the lubricant is not replenished occasionally.
The joint could be redesigned to prevent sticking without annual maintenance. But most designs introduce new problems that have so far discouraged adoption. For example:
The gap could be made larger by using a smaller post or larger seat tube, but the post would wiggle more and eventually damage the frame at the seatpost clamp.
A smaller seatpost could be used with top and bottom shims, and with the bottom shim of plastic, to allow wiggle without jamming from oxidation. This would increase manufacturing cost and be more parts to break or slip out of adjustment.
The seatpost could be made with a lower clamp. Doing so would add substantial cost and make it more complicated to adjust the seat height.
Removing and relubricating the post is quick, so the main disadvantage of the "annual maintenace" approach is many riders are not aware of the problem and thus not aware of the need for maintenance. The above bicycle was assembled without lubricating the seatpost, and was ridden for about a year.
Related photos from http://www.yellowjersey.org/goodn.html as of 2012/06:
As noted above, quill stems also sieze.