
Alrighty, as a long-overdue update on Zuzi Martinez's big handy guide, I will now attempt to consolidate all of the explanations, additions, and updates (e.g. Top Size → Taper) into one quick & handy new guide for all who would like to trim down their prims to look slimmer than the limit

FIRST, for all of you who like a good visual demonstration...
THE VIDEO: Torley's "How to make tiny prims – Video Tutorial"
@ http://www.youtube.com/watch?v=m6XqQM9hgB0
This alone could be quite enough to get you going tiny, but here are some pointers to help get your thoughts going all the better.
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THE BASIC METHOD: CUT 'N' HOLLOW
Let's start with the most evident answer to the problem, fairly easy to figure out if you just play with the shaping values in the Build window → More» → Object tab. Anything labeled "Cut" or "Hollow" can help you to cut away from your prim, so that although its "Size" (more like the 'original size') may be .01m each way, it can have much of that trimmed right off of it. On the three toroidal prim types (torus, tube, & ring), you can also squish the prim with its "Hole Size" settings.
THE HIDDEN HACK: "DIMPLE" IT
Imagine for a moment that your Cube, Cylinder, or Prism prim is like a sliced (or about-to-be-sliced) loaf of bread. Normally you work with the whole loaf, but you can also choose to work with just the first, last, or middle couple of slices, or most any range of slices really, if you uncover these two hidden parameters...
It's easy. Just temporarily change your Building Block Type (Object tab again) to Sphere. You'll see two "Dimple" values at the end, which default to 0.00 and 1.00 (that's 100%). Changing them will cut off part of the sphere, and when you change your Building Block Type back, will leave 'slices' removed from the ends of your 'loaf'.
This can be used in powerful combination with Taper, as the center (or especially top) slice of a pyramid or cone is smaller than that of a prism or cylinder.
IF ALL ELSE FAILS: USE ITS INSIDES
If the outside of your prim is just too big, maybe the inside isn't. So give your prim an inside surface by turning the Hollow value above 0. Then, using Select Texture and the Texture tab, make the outside disappear by selecting just the outside texture(s) and applying a full-alpha texture (freebie texture packs might offer something named "alpha" or "totallyclear"

To keep these innards from looking like innards, you'll either have to turn the surface direction inside-out, or give it very flat coloration. To completely flatten the color, in the Texture tab, make it Full Bright, then set the Texture to Blank, and apply a Color afterward if necessary.
NEW POSSIBILITIES: SCULPTED TININESS?
Sculpted prims give the appearance of any shapes you model within a limited cubic space. So, what if the modeled shape does not use up all of that given space? The resulting sculpted prim will be smaller than the size you set it to! Just avoid making it as small as possible, as there's a limit to how little you can model before the system says this is just too tiny, and defaults to a sphere. Also, the smaller you model the shape, the more detail you will have to sacrifice, making round shapes look rougher.
A quick & easy (though quite limited) place for anyone to start sculpting is ROKURO – http://kanae.net/secondlife/. If you use it to draw a rectangle smaller than the size of the window, you should end up with a cylinder smaller than your in-world specified size (likewise, circle=sphere, triangle=cone, and so on). For more sculpty-centric tools, check http://wiki.secondlife.com/wiki/Sculpted_Prims:_Resident-made_Tools.
If you already have a sculpt map that you want to shrink down, all you need to do is reduce the image's contrast, i.e. bring the whole image toward gray (the center color). Using a contrast adjustment tool or adding a gray layer on top of it should work just fine in any decent image editor (e.g. the free GIMP).
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Build these, then Ctrl-Shift-shrink 'em down as far as they go, and you'll see just how tiny they are.
THE BASIC TINYCUBE – 0.005 × 0.005 × 0.005m minimum
Start with a Sphere prim, just to set its Dimple values to .25 and .75 (although any values .5 apart will work). After that, change Building Block Type to a Cube prim, and change its Cut Begin and End to .125 and .375 (or .375 & .625, or .625 & .875).
THE FLAT LITTLE COIN – 0.005 × 0.005 × 0.00025m minimum
Use a Tube prim, and turn up Hole Size Y to 0.50 (making a hole-less cylinder). Trim down the size by setting Profile Cut to .375 & .625 (or .625 & .875). Finally flatten it by turning down Hole Size X.
Note: You will need to work with Planar texture mapping to actually apply a normal coin texture rather than a radial one. (Thanx Alia and Renee!)
THE REALLY FLAT SHAPE – Makes a tiny little •, ■, or ▲ – .0002m min. thickness
Start with a Sphere prim, to set its Dimple to 0.50 & 0.52 for .005m width, or 0.75 & 0.77 for .0025m width, etc. Switch to a Cylinder, Box, or Prism, and turn up Taper X & Y to 1.00.
THE PERFECT LITTLE SPHERE – ~0.000001m minimum diameter (that's 1 micron!)
Use a sphere prim, and a transparent texture like "totallyclear" or "alpha". Twist the sphere by the same 180 at both Beginning and End, and it will be turned inside-out. Give it some Hollow (which can be turned down as low as .01, maybe lower), and you will see a solid-looking little sphere in the center. Apply the transparent texture to the outside, and only that little sphere will be left to view.
THE LONG, THIN STRING – perfect for many string instruments – 0.00025m min. width
Use a Tube prim, and turn up Hole Size Y to 0.50 (making a hole-less cylinder). Hollow it out all the way (to 95). Remove the outside by Profile Cutting to 0.50 & 0.75.
The only problem is that the very ends are not flat, but pointed, like on a toothpick. This effect largely disappears if you turn down Hole Size Y to .48 or so, uniformly adding thickness across the string. You can also cut off one of the pointed ends by Profile Cutting to .125 (giving you half of the string/toothpick).
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-Remember that although you may see only, say, 3 digits past the decimal point, you may actually be able to edit prim properties to further detail (e.g. Path cut .0625, Hollow 00.05) just by entering the values in those fields.
-If the yellow/blue glowing halo around your prims gets annoying, then before loading up SL, you can change their color to transparent, as explained at http://www.garhunt.com/hunter188/html/fun_with_sl_ui.html.
-To make your round tinyprims render rounder, try making them out of prims with a larger original "Size".
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If you know anything at all I should add or fix here, let me know and I'll be glad to improve this tiny prim guide!