Converting/modifying ATX power supplies for benchtop use is a fairly well discussed procedure, but I've found no single source of documentation which covers the topic extensively from an engineering point of view.

Why would you do this?
ATX power supplies are mass produced, and relatively inexpensive. If you purchase new 300 watt PSU from Newegg you'll be paying between $20 and $40.
A 35 Watt benchtop supply from Agilent will cost you more like $700.
Admittedly, it's not an apples to apples comparison- the ATX supply will give you fixed outputs, whereas the Agilent will give you adjustments, but the ATX will deliver WAY more power, for WAY less money ($0.13 per watt, versus $20.00 per watt).
Since the ATX supply will deliver "typical" voltages (3.3, 5, 12, -12, -5 [sometimes]) the adjustment issue might not be particularly relevant.

The documents of interest
The ATX Specification v2.2, the ATX12V Power Supply Design Guide v2.2, and the ATX12V Power supply design guide v2.01. All of which can be found at FormFactors.org.
The ATX Specification v2.01 found at Intel.

What kind of quality can we expect here?
That's a good question, for which I refer to documentation--
For now, let's limit discussion to v2.2.
I refer you to the ATX12V PSDG v2.2, page 23, Table 12. We see that ripple/noise in the 10Hz to 20MHz range must be no more than 120mVpp for 12V lines, 50mVpp for 3.3V and 5V lines, 120mVpp for -12V, and 50mVpp for 5VSB.
If you go to Section 3.2 (pg 13) you'll note that all the signals must be regulated within 5% tolerance, with exception of -12V, which has 10%.
In terms of quality- this is pretty good. If I need better than this, I'm probably using my own regulators anyway.

What could go wrong?
That's a good question too. According to Section 3.1.5 (pg13) of the ATX12V PSDG v2.2 component failure shouldn't cause flame, smoke, charring, scary sounds or explosions involving melted stuff. But if you're using this thing bench top, you're probably more worried about what would happen if you accidentally shorted outputs.
Let's go to secion 3.4 (pg 29) of that same document. The supply should have significant short circuit protection with regard to rail to ground and rail to rail shorts. The supply shouldn't be damaged by shorting, so in theory at least, the worst you could do if you slip up is make the thing turn off.
Supposing you disconnected all the loads, the thing might turn off, or not power up, but it won't be hurt by this.

What could go really wrong?
Like all electrical systems, there is a potential for you to hurt yourself (check out the pun!). If you don't know what the risks are and how to mitigate them, you probably shouldn't be reading these forums, much less building a bench top supply. You don't have to be stupid to hurt yourself, you just have to make a mistake. Play careful.

What rails/signals are available?
ATX v2.2 specifies a 24 pin main connector, delivering 3.3V, 5V, 12V, -12V rails, a power ok signal, a power supply enable, and a 5V standby rail.

Additionally, the supply has "device" connectors in assorted flavors, offering the same 5V and 12V as well as a separately provided 12V.

"Interesting" signals:

Power OK (PWR_OK) is 5V TTL compatible. It goes high when the 12V, 5V and 3.3V rails are happy. Power OK isn't meant to source current. (Not even little bits. Sorry.)

Power is enabled by asserting Power Supply enable (PS_ON#) which is low true, TTL compatible. It's asserted by shorting/driving to ground and can be left open to disable. Enabling this signal turns on the supplies primary rails. This signal has no control over 5VSB.

5VSB is the 5V "standby" supply. This is always enabled whenever the PSU has input power. In the v2.2 of the spec, it should be able to supply 2.5A. In a "real" system, the standby supply is used to power the system when it's turned off. Your power button doesn't turn the supply on, but tells some asic on the motherboard to turn the supply on and power up the unit.

Differences with older supplies
Older supplies of the ATX flavor (such as v2.01) used a 20 pin connector rather than the 24 pin for primary power. Notable differnces include that v2.01 had a -5V rail, v2.01 had only one 12V rail, and the v2.01 specified VSB supplied significantly less current, mandating only 10mA.