Engineer
Gun Wrangler.
Advantages
Sentry Gun, can re-arm other defenders.
Disadvantages
Poor armour, lacks firepower
Health
80
Armour
50 (spawns with 25)
Typical role
Defence.
Notable Weapons
Spanner (that's a wrench to all the Americans out there)
Use it to upgrade, repair and reload sentry guns. It can also be used to repair your team-mates' armour - just hit them with it.
Railgun
Not, unfortunately, remotely related to its Quake namesake. Think of this as a slow-firing nailgun. However, each bolt does more damage than a standard nail, and will scythe through armour. This weapon is a very effective long range sentry gun killer.
EMP grenade
Generates a localised field which detonates all explosives in range, excluding resupply packs, but including discarded ammo packs, pipebombs, and unexploded grenades. This can be devastating for heavy classes, as all the explosives they are carrying explode - which can create a huge blast in the case of demomen.
A popular tactic is the suicidal EMP run - prime an EMP grenade, and then go and give the victim a big hug. The engineer is quick enough that most heavy classes will not be able to escape. If the Engineer discards ammo first, he may even survive the blast (but probably not if his target is a demoman). The golden rule is to remember that the EMP will only affect targets carrying explosives - a scout only has to discard ammo (thereby dumping any rockets he has acquired) to render himself all but immune to EMPs.
Offensive capacity
Some. The Engineer's railgun is a surprisingly effective sentry-gun killer, delivering lots of damage rapidly to long range. His EMP grenades can also wreak havoc against many defensive schemes, but his lack of real speed, armour or firepower is a big handicap.
Defensive capacity
Excellent. Although the engineer himself is a fairly weak fighter, he can build a sentry gun - the single most effective defensive weapon in the game. Level 1 Sentries are pretty useless, but level 2 guns are a real threat to all classes and level 3 guns are very dangerous indeed. Real thought should be applied in choosing the position of the gun, and teamwork by the remainder of the team is essential. A solitary Sentry is just grenade fodder, and won't last long. Guard it with a soldier, however, and any attacker will have a real problem.
The way to spot a really good engineer, though, is how they work with other defenders. In military terminology, an engineer is a force multiplier - he makes the other defenders more effective. In between building and maintaining a sentry gun, a good engineer will be repairing his team-mates' armour and keeping them stocked with ammo, either directly or via his dispenser. This can make a huge difference to the effectiveness of defenders who are posted a long way from resupply areas.
How to fight them
Neutralise the Sentry Gun. Their static nature makes them particularly vulnerable to grenades and long-range attack with Rockets or Nail/Railguns.
In a straight fight with an engineer, just apply firepower - they have less armour/health than any class but the scout. Be careful, however, to listen for grenades being primed (it may be an EMP) and not to forget where his sentry gun is.
Some classes can render themselves immune to EMP grenades by discarding all their explosives (i.e. grenades and rockets), but this isn't really viable for many classes (Demoman and Soldier in particular) since this will leave them almost completely unarmed.
Tricks:
Exploding Dispensers
Engineers can bind a key to remotely detonate their dispenser, turning a fully loaded dispenser into a very powerful remote-controlled bomb. An alert player can therefore build a dispenser in a carefully-chosen position, and use it as a last-ditch defensive weapon.
Use Yourself As Bait
It's amazing how many offensive players, once engaged in a one-on-one fight with another player, will keep duelling while the defender backpedals, and thus get lured into the fire-zone of a nearby sentry gun. Of course, you don't have to be an engineer to pull this trick off.