What does it mean to say that a train is "N scale"? Basically it is telling you how big the thing is compared to the real item that it models. Carl Arendt has a complete list of the scales and their dimensional meanings at http://www.carendt.com/articles/scaleguide.html, archived here. Scale also implies other things, such as coupler design, that are standards associated with the scale. However, it is not quite that simple.
This scale has really only just become a "standard" in the naughties. The Eishindo Company of Japan created a series of models, the 103 series, in 2006. Unlike its predecessors, it has not failed almost 8 years later, and it has a Wikipedia Page, so I guess as of 2013 we can call it a standard scale.
T-scale models are made with a ratio of 450:1. T stands for Three, as in "three millimetres", the width of the track. A locomotive that is 75 feet long in reality would be 2 inches long as a model. The minimum turn radius available in standard track is 120mm or 5 inches. This is the equivalent of having a real-world, full-size track that turns with a radius of 54m, when scaled up.
This scale is built with a ratio of 1:220. This means that a 75-foot-long locomotive comes out measuresing 4 inches. The rails of the track are 6.5mm---about 0.25"---apart, so the real rails would be 1.4m or 4.7' apart (close to the real-world standard of 4'8"). The nominal minimum radius of curvature---the tightest standard curve made---is 6" (150mm). This is the equivalent of having a real-world, full-size track that turns with a radius of 33m, when scaled up.
From the 1970s to the 2000s this was the smallest scale made in commercial quantities. It was introduced by the Marklin company in the early 1970s, and they remain the only major company making a complete range of Z-scale products, though at least one other manufacturer makes the trains and several make scenic accessories.
Tomix make N-scale curves with 103mm (4") and 140mm (5.5") radii. These correspond to 17m and 22.4m in the real world.
The old OO scale is close to, but not quite the same as, HO scale, but uses the same model rail dimensions.
Here trains are built to a ratio of 1:48, so the 75-foot-long locomotive is 18.75 inches long. The rails of O gauge track are 1.25 inches apart. A minimum turn radius of 13.5" (345mm) corresponding to 16.5m scaled, is available, although the normal minimum is closer to 15.5", or about 19m real-world turn radius. In either case, this is abnormally tight.
Strictly speaking, the "O27" gauge that provides the tighter radius noted above is a different scale, about 1:64, but this mere detail is often lost or ignored. I assume this is because of the advantages of the tighter dimensionality.
These trains are built to a ratio of 1:22.5, sometimes 1:24, while the Marklin "maxi" or "1" scale is at 1:32, although the track is always the same width. In G scale the 75-foot-long locomotive becomes 40 inches long. G and other large scale trains run on gauge 1 track with rails 45mm apart. Note that the real-world equivalent spacing of the rails varies with scale, but then so did train tracks vary with place and era. The minimum turn radius of 24" (610mm) corresponds to a startling 14m scaled, although it is acknowledged at a lot of rolling stock modelling longer items will not handle the minimum radius.
Most narrow gauge railroads in Colorado were 36" gauge between the rails. HOn3 would be HO Scale with 3' between the rails. (Standard gauge is 4' 8.5" between the rails.)
It is clear that the limit is "pushed" hardest in G scale. The limit is not firm; as the turn gets tighter and tighter, more and more rolling stock becomes unable to negotiate the turn, or the length of train that can make the turn gets shorter and shorter. If you limit your rolling stock, you can reduce your minimum. G-scale items are often short (4-wheel locos, etc.) and thus more amenable to tight turns. Perhaps this is because truly long items are awfully big in G!
The coupling between carriages typically forms a hard limit. Tighter turns would require a more acute angle between the axes of subsequent coaches, and buffers or coupling mechanics reach the end of their travel.
The implication from G-scale is that there will be trains that can negotiate a turn of about 3" diameter in Z or 4" in N-scale, couplings permitting. Many of the layouts featured in Carl Arendt's site rely on using limitingly tight radii of curvature.
Here are a set of locomoties, the same model
in Z, N, HO, O, S, and G scales.
This is the image I had printed for display at a microlayout exhibit. It shows a Mallard A4 locomotive scaled correctly into various popular scales. Note the small print just below the image at T scale... this is a line 1" or 25mm long. If displayed such that the line is 1" long, the pictures will be the correct size. This may put them in better perspective! (Requires a poster-size printout and a high-quality original image.)