Oh, you all are singing my tune!  Here's my old hooptie:

That's a stock photo, but I have a pic of my actual tank somewhere on my home computer.  Between that and the M113A3, I had all sorts of fun in the Army!
Now, in my brigades, combat engineers weren't responsible for recovering downed tanks;  that was the maintenance folks, who drove M88 recovery vehicles.  We also didn't do carpentry, drilling wells, building schools, or all that other stuff;  we were COMBAT engineers.  Which is to say, "infantry with a shovel".
The combat engineers in the brigades I was in were responsible for three missions:
* Mobility:  Breaching obstacles, blowing minefields, clearing booby traps and IEDs, bridging rivers and tank ditches, etc.;
* Counter-mobility:  Emplacing obstacles, minefields, abatis, and booby traps, blowing bridges, cratering roads, etc.;
* Survivability:  Digging fighting positions, entrenching infantry, building hasty fortifications, etc.
Our vehicles were designed to accomplish these missions:
+ The M728 CEV was equipped with a boom, a dozer blade, and a 165mm breaching gun, which fired an enormous High-Explosive Plastic (HEP) round that could demolish a bunker from 900m.  It was also an excellent vehicle to use in MOUT support of dismounted infantry.  It has since been replaced by the Grizzly CEV.
+ The M9 Armored Combat Earthmover (ACE) is employed to dig fighting positions and also push through obstacles.
+ The M548 Volcano mine-dispensing vehicle is a tracked truck with tubes of scatterable, self-arming mines.  It could lay out a 200m minefield in just a minute or two, with a mix of AT and APERS mines that could also be set to deactivate themselves after a set period of time.
+ The Armored Vehicular-Launched Bridge (AVLB) was an M60 chassis that mounts a 20-meter assault bridge, for relatively quick crossing of tank ditches and blown bridges.  It has since been replaced by the Wolverine bridging vehicle.
+ The Mine-Clearing Line Charge (MICLIC) is a rocket-propelled canvas hose filled with 1,500 pounds of explosives.  It's fired from a trailer or M60 chassis across a minefield, then detonated to destroy a lane through the minefield.  I have some wicked danger-close pics of MICLICs going off on my home computer, and I'll post a couple when I get home.
I've always enjoyed making sure my boys were represented in my games.  I've converted a 15mm Komodo APC from DLD Productions as a combat engineer vehicle for Stargrunt, and I'll see if I can find some pics of it to post.  I also have some plastic Epic Rhinos that I've dressed up with GZG boom arms and Epic dozer blades for use in Dirtside;  I'll have to see if I can find them and snap some piccies.
Altogether now, to the tune of the Battle Hymn of the Republic:
We are, we are, we are, we are the Combat Engineers,
We blow a lot of demo and we drink a lot of beer!
The infantry and armor boys need never have a fear,
For here we come! You know we are, the Combat Engineers!