There's some confusion and many questions about slotted bridges. This page will, hopefully, help answer some question and clarify some terms.
First, let's define "slotted bridge". The way I use the term, a slotted bridge is one in which a slot is cut for the string in the actual bridge, all the way thru the bridgeplate. Ideally, a non-slotted pin is used in conjunction with the slotted bridge. The opposite approach is to leave the bridge hole round and cut a slot in the pin. This is what you find on most new factory guitars, with some exceptions (many small builder guitars- Collings, for instance- are slotted, fully or partially). On the left, we have the inside of a non-slotted hole. You can see that string rides in the groove in the pin. (and just to the left of it is a slotted hole....). On the right, we have a slotted hole. You can see how the slot is cut for the string and fits it pretty closely.
(above) This is what it looks like when the strings are pulled tight against the bridgeplate (the bridge itself in this case). It's not a huge difference, but you can see that the ball on the left is trying to push itself into the groove in the pin. Over time, the hole can wear and get larger and the ball-end can start working its way thru the bridgeplate. Plus, the pins tend to bend backwards (see picture below). The right ball is in a slotted hole, pushing against a non-slotted pin. It's locked in. The pin itself is stronger, too, with a solid side facing the ball.
Here's what it looks like with 3 slotted holes/non-slotted pins (left), and 3 non-slotted (or partially slotted) holes/grooved pins (right). There is a MUCH larger overall groove on the right and the ball will, over time, work its way into that groove.
This is what typically happens to grooved pins, esp. plastic ones. The ball has bent them backwards, making them pretty tough to remove and letting the ball end work its way up thru the bridgeplate. I'm not saying this doesn't happen with slotted holes, but I am saying it doesn't happen as much.
Advantages of slotted bridges:
1) the ball end is supported securely on 4 sides- 3 by the bridgeplate, and 1 by the non-slotted pin.
2) I think they sound a little better. I've done nothing but slot a bridge on a customer's guitar and he (skeptically) played it for an hour and thought it had a little better definition and clarity. Just a little, but, hey, do you want a little or not? I'll take it!
3) I think the bridgeplates last longer since the ball end isn't trying to work its way up the hole. On a correctly slotted bridge, you can sometimes actually remove the bridgepins while the strings are under tension. I like to have just a little "push" on the pins to help hold them in place, but you can definitely feel the string "click" into the plate.
4) every Martin guitar that I've examined built prior to 1985 with the original bridgeplate has a slotted bridge, although the low E might need just a little more opening up. If you can turn the pins around so that the slot faces the rear with the string in place, the bridge is slotted.
The one caution I have with slotted bridges is that you string up your guitar right. Since the slot pretty well matches the size of the string, it's easy to get the winding hung up and leave the ball end suspended in the guitar (right ball).
This will cause a very irritating buzz as the ball end slaps against the pin. The way I like to string up slotted bridges is to put the ball about 1/2 way into the hole and then use the pin to push it the rest of the way in. More on stringing here: Stringing.
"Ramping" is a whole 'nother issue. A bridge can be ramped but not slotted, not ramped but slotted, both ramped and slotted, and neither ramped nor slotted! A "ramp" is when the top of the bridge is cut so that the string moves closer to the saddle and thus changes the "break angle" over the saddle. The bridge on the left is slotted but not ramped, and the bridge on the right is slotted and ramped. Note how the string slots are cut toward the saddle in the ebony bridge. The ramps do NOT go all the way thru at this depth, but simple make a little trench for the string.
Compare the break angles of these two shots. The one of the left is (essentially) non-ramped. Notice how the string dives into the bridge at the base of the pin. In the right picture, the string is ramped and dives into the bridge a little distance away from the pin, creating a sharper angle over the bridge. A sharper angle is not necessarily desirable, but what's important is that we can use the ramp to control the break angle. We usually get the best "bite" on the saddle and best sound as the angle is right around 45 deg, plus or minus some. [note that this is the same hole in both shots. I pushed a toothpick in the slot to "de-slot" it- this is a useful technique- and under string pressure, the toothpick squished. If the hole were truly non-slotted, the string would actually dive into the bridge IN the pin, creating even less of a break angle. Hopefully, though, you'll get the concept from these pictures]
This is a case where I used ramping to change the angle of the high E string. On Martins, the high E and B are much farther away from the saddle than the low E and A strings. You can ramp them up just a little to more closely match the angles, and thus create a little more even pull on the saddle. This break angle really does change the sound just a little. In the left shot, the hole is non-ramped and the high E has a much shallower angle than the low E. By doing a little light ramping, I changed the angle to more closely match the low E, adding just a little bit more treble "snap" in the process.
Notice the angles on this Collings guitar. Instead of drilling holes in a straight line and angling the saddle like Martin does (on most models), Collings angles the holes to match the saddle. This keeps the holes off a single grain line and helps prevent splitting, but it also creates very consistient break angles for all the strings. Check out the low E on this guitar- see how it "humps" up a little compared to the others? That's because the thick E winding can't bend sharp enough. A very slight ramping of the low E would bring it down to the angle of the others (and, since this is my guitar, I'm going to go do just that!). Martin uses this same techinique of angling the pins on the 1-series guitars (D1, 000-1, etc.). This Collings guitar (a 1992 Brazilian/Adirondack Clarence White), by the way, came from the factory (John Holman, actually) with a slotted bridge, slight ramps, and non-slotted pins.
See an Actual Case and how I fixed it....