I'll try to set the scenario for you with details that I think may be connected.
97 Bonneville SSE, 130K+ miles and has had this problem for the last year or so.
I have run through several searches in the forum, and at least the ones I read didn't match my cars symptoms quite exactly

Starting off when cold or near cold and sometimes when at operating temp, pull out of driveway and down street to highway, stop, pull onto highway (50 mph zone) and when ramping up to speed or when aggressively attaining the speed limit the engine seems to bog so significantly that we often need to pull off to the side, it idles fine.
If I put it in park or neutral and gently accelerate the engine it will raise on the tach to 3-4K, no more, it will rise an fall consistently. If I mash the throttle it seems to do the same, similar to a diesel "governor hunting".
Now I have also gone for a ride up the street where there is no traffic and noticed that when these same set of circumstances occur, the trans has no output what so ever, just coasting and slowing down as engine falters around 3-4K.
A possible connection? Trans problem and the engine is told not to give output?

The check engine light comes on during these episodes. I arraigned for my wife to take it to a GM dealer and run a diagnostic on it, ($80) and all the gave me to go on was an EGR code and said they would replace it for well over $200.
I bought a gasket and cleaned the sticky EGR with Seafoam until it wouldn't stick at all, installed with the new gasket and tested after only a 3 minute warm up, same problem still, but the EGR is at least clean.

130K+ miles, 2 year old coil pack, wires 6 mo. old plugs, 2 year old replacement chip from dealer, new fuel filter and oil change.
Trans was rebuilt 2 years ago and I noticed that it wasn't pulling up the same amount of acceleration after breaking in period and it never did shift the same, would sometimes rev way high until a hard shift to second, and also when at 40-50 mph and mashing the pedal there would be a long delay before downshift which was almost immediate before the rebuild.
There has also been a regular stumbling, or hesitation when starting from a stop, and if I let up on the throttle right away it will often die.

This all happens a little less frequently with regular use of Seafoam in the medium grade gasoline, but the underlying problems still occur.
If I had the test equipment or could afford to have it in the dealer for extended tests I would have, but for the most part these symptoms are annoyances that I can put up with, but my Wife can't....
Thanks for whatever input you may have.

Can you put "97 SSE" in your signature? Thanks!

The 94 and newer linear EGR'* don't respond very often to a cleaning. The older digital EGR'* do. So simply cleaning until it doesn't stick may not do it for you. I'd suggest an EGR from a wrecker to swap in at this point.

Your driving symptoms are right in line with the EGR possibility.

On the overall problem. Have you kicked your cat lately? j/k

Bogging during hard acceleration or periods where there would be a lot of exhaust. Look into the catalytic converter as a possible problem. Typical signs would be rattling when hit/kicked, poor economy as the engine fights to push exhaust through it and restrictive exhaust.

Thanks guys!
I was busy running around today, not to mention not feeling very well so I will check out the cat issue tomorrow.
Any leads on cat replacements?

CHECK your cat, but I believe you'll find you have an EGR issue, considering the Cat can't cause an EGR fault, and Cats don't normally cause issues until the car is well heated up. You may have both problems, but the code is pointing to EGR, as are your symptoms.

Well I kicked the CAT and heard nothing, but that just means it ain't broke to me.
I just took it into the trans guy I had rebuild it, he drained, flushed, replaced the filter and checked it all out, certified it okie dokie!
(For $132)
The car immediately started running gutless so I turned around within a block and had him drive it. He suggested that it was a clogged CAT and told me to go to one of several muffler shops, which at five to five o'clock isn't an option. My Wife and I went home, and I turned around after a brief stop there and went to a mechanic buddy who recently left his former shop to start his own, specializing in under body work, but has the tools to do most everything.

He whipped out a SnapOn OBDII test unit and started going through things. No codes showed so he checked into several other items, he found that the unit recommended a 40 - 65 psi. fuel pressure so he got his gauge and began to check.
The best pressure it would put out was 34 psi. not good, so his other guy agreed to be in on Saturday to drop the tank and replace the fuel pump.

In about 1.5 hours it was done and we started it up. First at about 45 psi. and running obviously rough still. But after running for about 10 minutes the air must have purged out of the line as it was above 50 psi so far and it was running really well. ($140 for the pump and screen, $125 for the labor - he earned that for sure!)
So, I took it our for a test drive and it was a huge difference! The trans now kicks down properly and acceleration is right back where it should be.
So far so good!
There is, however, an intake suction sound when you first stab the throttle and a hesitation. This sounds like it is from the rear of the engine, and soundl like an open 2bbl carb sucking, ya know? It seems to be at or around the EGR to the middle area, but there isn't anything obvious as far as lines off, broken or loose, so we decided not to waste time on the clock on it, I can look more later in the driveway.

The momentary hesitation if you stab is is controllable if you ramp it up like normal, but I will eventually find that one too I hope.

So live and learn guys, thanks for the tips too!

By the way, the cat was still performing well, good temp differential from front to rear, rear being the hottest.
Thanks, Gary