Traditional electric stoves have a drip pan under each burner. (Neither gas stoves nor flat-top electric stoves are covered here.) The drip pans can always be removed easily, often by tipping the burner element up slightly and pulling parallel to the stove top on the higher side until it disconnects. They can and should be cleaned periodically ...especially after a cooking pan has boiled over. But the day will come where they can't be cleaned any more, either because they're partially worn through or because the encrusted gunk is adhered so well you can't wash it off. When the drip pans can't be cleaned, they should be completely replaced; new ones are readily obtainable.
The first thing you'll notice when looking at your stove —or at packages of replacement drip pans— is there are two sizes. The large size is often called 8 inch, and the small size is often called 6 inch. (There is also an extra-large size, possibly called 8½ inch. But it is so uncommon that you'll probably never see one.) You'll generally see both sizes on a stove, 2 large and 2 small on most newer stoves, and 1 large and 3 small on many old stoves.
The quality of burner elements is mainly indicated by how many times the heating element circles the center (more turns indicates higher quality). The number of turns varies from two to four for small burners and three to five for large burners. Generally, although porcelain-coated drip pans may look nicer and be easier to clean in the short term, they won't last as long. It's usually difficult or impossible to know how thick/heavy a metal drip pan is; the only rule of thumb I can offer is you get what you pay for — really cheap replacement metal drip pans are often so thin they won't last very long.
6 inch and 8 inch are approximately the outside diameters of the heating element —or the recess in the drip pan into which the heating element fits; the largest outside diameters of the drip pans are roughly 7½ inches for the small and 9½ inches for the large.
Large and small are pretty obvious, are approximately the same on all stoves, and are not a problem (beyond the obvious that a small drip pan won't fit under a large burner, and vice versa). You needn't worry about them (except that a set of 2 large and 2 small drip pans obviously isn't going to satisfy a stove with 1 large burner and 3 small burners).
But there are also micro-size differences, which are too small to be measurable, yet large enough that not all drip pans will fit your stove properly. These micro-sizes matter a whole lot more than the large and small sizes. And unfortunately they are almost impossible to identify by measuring. Element micro-sizes are getting more and more standardized, so a universal heating element or drip pan is likely to fit any new stove. Do not just assume though that any heating element or drip pan will fit your stove simply because it's large or small. (The remainder of this discussion focuses on drip pans only, simply assuming you've already got the right heating elements.)
The drip pans for the small burners are similar enough that often the wrong micro-size will fit anyway; the wrong micro-size is more likely to be evident on the large burners. An incorrect micro-size drip pan may be too deep or slightly too big to fit in the hole in the stovetop; may clatter around; may not sit level, often rocking when a pan is placed on the burner; may make its burner element unsteady; or may not support its burner element at the expected height.
The differences between micro-sizes are too small and too variable to measure reliably. Fortunately in most cases you can figure out which drip pans you need simply from the brand (and sometimes the model number too) of your stove. Most sales points will tell you for sure whether or not particular drip pans will fit your stove when you simply supply your stove's brand and model number.
Some burner elements are hinged, which means they cannot be completely removed easily, but rather can be tipped up while remaining connected far enough to remove the drip pan from under them. Drip pans for hinged burners have a cutout all the way through their top edge for the burner element electrical connections, and often a separate trim ring to cover that cutout. Both hinged and non-hinged burner elements can be disconnected by pulling them away from their attachment point, and reconnected by pushing them back in to their attachment point. Hinged burner elements are becoming increasingly uncommon.
Sometimes different kinds of drip pan are described by Style-A (or Type-A), Style-B (or Type-B), and so forth. Style-B is for stoves from GE or Hotpoint (or other brands manufactured by them: Moffat, Monogram, Profile, RCA, or Roper). The very slightly smaller and shallower Style-A is for stoves from all other manufacturers (Kenmore, Whirlpool, Frigidaire, etc. etc.). Style-C is for stoves with hinged burner elements made prior to 1995 by GE/Hotpoint manufacturers. Style-D is for stoves with hinged burner elements made after 1995 by GE/Hotpoint manufacturers, and has what's called a step-down so the burner element sits deeper. Style-E is for stoves with hinged burner elements made by any one of the other manufacturers. And Style-F is for Canadian electric ranges. A Universal drip pan is even more of a wild card than the Style-X categories, as there's not even a definition to be ignored.
Unfortunately this Style-X system is not standardized, and is not even used at all in many cases. About the only thing you can be sure of is the diameters and depths of drip pans labeled Style-A or Style-B. There are plenty of inconsistent uses to trip you up, for example a drip pan for a hinged burner made by one of the other manufacturers, which it seems should be called Style-E, is sometimes instead described as Hinged Style-A. And Universal drip pans often differ from each other. So, other than very simple cases whose micro-size is Style-A or Style-B (or perhaps Universal), do not rely too heavily (certainly not solely) on this system. Instead use your stove's manufacturer and model number as a reference to get the right drip pans.
So what's the right size drip pans for your stove?