Clicking noise, 2004 Toyota 5-speed

The only way to find is first jack up each wheel and spin it. Look at the back of the tyre and the wheel. Also look for fallen wheel well guards. It can even be a stick picked up after driving through a puddle!

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Could be a number of things, bad CV joint is one of the first things that come to mind. Does the sound increase when you turn left or right?

When EXACTLY do you get this sound? Does it change when you rev the engine? Does it change with road speed? If this is happening when you are parked and in Park/Neutral DO NOT drive this vehicle until you have fixed this issue. This means that this is possibly a serious engine issue.
If it only happens when you are moving it is likely to be a transmission or suspension issue.

Is it a "tinny" sound? If so its probably a heat shield.

Hello
The Engine and Automatic Transmission (not applicable to manual transmissions) in this vehicles drive train are fully electronically controlled by a computer called the PCM and TCM (Power Train Control Module, Transmission Control Module). When a problem like this or other drive-ability related problems occurs the computer stores a record of the problem (there are of course some exceptions to this, like the fuel pump, engine coolant temperature sensor and MAF sensor for instance) in the form of a fault code in its memory, to read these fault codes you must have the systems memory scanned with a special tool. Once the fault code(s) are read you then must perform the appropriate diagnostic testing to find and resolve the problem(s) DO NOT REPLACE ANY PARTS UNTIL A TRAINED TECHNICAIN HAS DIAGNOSED THE PROBLEM TO AVOID SPENDING YOUR HARD EARNED MONEY ON PARTS THAT MAY NOT CORRECT THE PROBLEM. Also always check fuel pressure for correct spec for your make and engine type.

have the drive shafts checked for failed cv joints , worn out disc pads and suspension rubber failures
Your "loud noise " comment is too generalized to get more exacting advice

Exhaust pipe pulling apart slightly at increased load?
or......increased load on bad drive shaft U joint causing noise?

Yes, your theory sounds right. You'll need to remove the blower motor or a cover on it to visualize the squirrel cage and remove whatever is causing the noise. In some vehicles there is a cover under the hood, which when removed, will allow you to inspect the blower housing. If no such cover, you'll need to remove the blower motor.

Sounds like your CV axle is worn out and making noise. Time to replace it.

Depends on what year and engine you have. But if the noise is only occurring when the vehicle is in drive, or reverse, then I would consider asking a local transmission specialist take a look at it.