All transition metals exist only in +1 state (or a close approximation thereof)

Yes, I know; reading this statement might make people think that megagallons of ethanol are coursing through my arteries. It sounds quite counterintuitive. But I have become convinced that this is the case. I have not explored the matter in exhaustive detail, and some questions still linger. The explanation can get long-winded and I will reserve it for sometime when my own thoughts are clearer. But here's the summary.

There is a very simple reason why all transition metals will prefer only the +1 state in their complexes; Pauling's electroneutrality principle.
More simply put, consider this; won't it be improbable for a charge of +2 or +3 to accumulate on a metal ion? There will be repulsive destabilization. We know that charge tries to disperse itself and stabilize any system. So this positive charge will try to redistribute itself and get delocalized, thereby making the system close to electrostatically neutral. Where can it do this? Well, we don't want to forget 'the other half'- the ligands. What this means is that it's actually the ligands that are getting oxidised by helping to delocalize the positive charge. So even in a compound like AuCl3, the Au has a +1 charge, and it's really the chlorides that are getting oxidised.

The whole root of the problem is that chemists' definition of oxidation state actually is quite arbitrary, based on qualitative notions of electronegativity. We think that since chlorine is more electronegative than gold, it will carry all the negative charge. But Pauling's electroneutrality principle tells us otherwise.

However, this is not something we usually think about. Consider the simple ammonium cation. Organic chemists depict it with the positive charge on nitrogen. But it's a well-known fact that the positive charge in fact is distributed over the hydrogens. Any system will try to stabilize itself by dispersing charge as much as it can. That's what the ammonium cation does, nicely dispersing the positive charge over the hydrogens.

We might say; but how can halogens get oxidised? They are supposed to be among the most strongly oxidising elements. But note, that this statement applies to diatomic halogen molecules, not to halogen ions in solution.

You can take my word that even the fiercely electronegative CF3- anion in the complex [Cu(CF3)4]- is oxidised, and that the copper exists as Cu(I) in this state. Even a look at the formula suggests otherwise; the Cu must be existing as Cu(III). But you don't have to take my word for it. Consider this publication in Angewandte Chemie. There was also a small debate, published in another issue of the same journal, which further combs some fine points and definitions and clarifies things. High level calculations strongly suggest that the Cu exists as Cu(I).

High level calculations, but more logically, the electroneutrality principle and basic concepts of electrostatics.

The point is, many things in chemistry are defined either arbitrarily, or with respect to some standard. Based on the existence of another chemical species, many things can change for a given species. Given the right conditions, almost anything can get oxidised or reduced. Given the right conditions, anything can be made stable. After all, nobody had thought that stable carbocations could exist. But George Olah opened up an entire new field of carbocation chemistry with his pioneering work. In chemistry, there are no absolutes. Which again proves why it is so interesting.

Actually, it's simple to think about. Usually we assume that the metal is changing its oxidation state. Instead of that, let's adopt the other perspective; the metal makes the ligand change its oxidation state. The result is the same. We still see AuCl3 in solution. But it's really the Cl- that has changed, and not the Au.

Some questions still linger; then why do all these metals seem to exist in different oxidation states. More importantly, how can one prove this contention by experiment? After all, ours is an experimental science.

But even in the absence of definite experiments, if one ad hoc concept is taken for granted, then another ad hoc concept surely cannot be worse. Especially if it sounds more logical and convincing. Like all metals existing only in +1 oxidation state (or something close to that).

Important addendum: I should mention that when I say +1, the actual number is better defined as "close to +1". Calculations show that it can change from +0.7 to about +1.2 (this bears on the question d_orbital asked in the comments) depending on the ligand environment. Thus, in hemoglobin for example, in the oxidised and reduced form, Fe won't exist as exactly +1 both of the times. Its oxidation state will fluctuate between decimal places close to one.
And, as Mitch quite rightly says, in most of our daily life, metals have an unequivocal oxidation state of 0!!