Updated 12.04.2010

We will look at some examples.  In Europe there are at least two ways of "counting" the axels and an American one.  There may be even more, that I do not know anything about, so please send me an e-mail if you know something more.

Locomotives with the drive shafts supported directly in the locomotive chassis:

Märklin 34831, LAG 895:

This is a Bo locomotive.  Two individually driven axels, without any mechanical connection between the axels.
B means two driven axels. o means separately driven.
If only one axel was driven it would be a A1 or a 1A, depending on if the front or rear axel was driven.
Driven axels are counted by letters, A=1, B=2, C=3 etc.

Märklin 26471, S.N.B Limmat:

This is a 2' A locomotive.  Two non driven axels separately supported and one driven axel.
The tender seems to be 2.

Märklin 3145, SNCF Y 50 101:

This is a C locomotive.  "C" means three driven axels are mechanically connected, in this case with rods.  In case of rods, often one axel or a jack shaft is driven by the motor.

Märklin 2857, Könische Württembergische St. E. T5 1205 :

This is a 1' C 1'.  In Switzerland 3/5 (three driven axels of total five), in America 2-6-2.
1' indicates that one non-driven axel is supported in a separate frame, not in the locomotive chassis itself.
Non-driven axels are counted by numbers, the ' indicates it the axel(s) are not supported directly in the chassis, but in some kind of "sub frame".  The sub frame is supported in the chassis.

Märklin 37131, SBB Eb 3/5 5818:

This a Swiss 3/5 (three driven axels of total five), in America 2-6-2, otherwise 1' C 1'.

Märklin 26831, ÖBB 86 106:

This is a 1' D 1' locomotive, in Switzerland 4/6, in America 2-8-2 (two non-driven wheels-eight driven wheels-two non-driven wheels)

Märklin 3308, DRG 85 006:

This is a 1' E 1' locomotive, or 5/7, or 2-10-2

Märklin 3417, NSB 63 2770:

This is a 1' E locomotive, 5/6 or 2-10-0
The tender is 2' 2'

Märklin 3100-2, DRG 03 124:

This is a 2' C 1' locomotive, 3/6 or 4-6-2

Märklin 3310, DB 012-081-6:

This is also a 2' C 1' locomotive, 3/6 or 4-6-2
This time the tender is 2' 3 (no ' after 3), as the three rear axels are supported in the tender chassis.

Märklin 39050, DB 03 005

This is a 2' C 2' locomotive, 3/7 or 4-6-4

Märklin 3100-1, DRG E04 17:

This is a 1' Co 1' locomotive, 3/5 or 2-6-2
Co because the three driven axels have one motor each and are not mechanically connected.

Locomotives where the axels are supported in separate bogies, the bogies are supported in the locomotive chassis:

Märklin 3772, DB 212 225-7:

This is a B' B' locomotive
B' means that two driving axels are supported in one bogie, and that they are mechanically connected.  There are two bogies.

Märklin 39420, SBB Re 4/4^I 10 015:

This is a Bo' Bo' locomotive, SBB calls it 4/4
Bo' means that two axels are supported in one bogie.  Each axel have it's own traction motor.  There are two bogies

Märklin 37320-1, SBB Re 6/6 11 687:

This is a Bo' Bo' Bo' locomotive, SBB calls it 6/6
Bo' means that two axels are supported in one bogie.  Each axel have it's own traction motor.  There are three bogies

Märklin 3137, NSB Di3a 3.623:

This is a Co' Co' locomotive, 6/6 in Switzerland
Co' means that three axels are supported in one bogie.  Each axel have it's own traction motor.  There are two bogies

Märklin 3300-2,  DB 194 155-8:

This is a Co' Co' locomotive
Even though the front and rear end of this nice locomotive seems to be separate parts, they are axel wise considered to be like bogies, thus Co' Co'.

Other combinations:

Märklin 26730, SSB Ae 6/8  13.304:

This is a (1' C) (C 1') locomotive, SBB calls it 6/8.
(1' C) means that one non-driven axel is supported in a "sub frame" which is connected to the chassis, and that three connected driving axels are supported in the chassis.  The brackets indicate that there are two separate wheel groups, individually supported in some central part.  It means that this is a "three piece" locomotive.

Märklin 3068, NSB Di3b 3.641:

This is a A1A' A1A' locomotive
It looks like a Co' Co' (like NSB Di3a), but in this case the center axel of each bogie has no traction motor.  In Switzerland this would be a 4/6 locomotive.

Märklin 37591, SBB Ae 8/14 11801:

This is a complicated one.  Both  (1A)A1A(A1) + (1A)A1A(A1) and (1'A)A1A(A1') + (1'A)A1A(A1') are mentioned in different literature.  In Switzerland it is simpler, just 8/14.
One non-driven and one driven axel separately supported, two driven axels in the chassis with one non-driven between them, and finally one driven and one non-driven axel separately supported. If that isn't enough, it's a double locomotive. The "+" connects the two parts.
The layout of the Märklin model is 1' Bo' 1 Bo' 1' + 1' Bo' 1 Bo' 1'.

Märklin 3148 x2, double traction NSB Di5 5.865:

This home made double locomotive combination is a C + C locomotive, or maybe just two C locomotives?

Märklin 3346, double locomotive DB 236 405-7 + 236 406-5:

This double locomotive is C + C.