Forge

The Forge provides you with the ability to research upgrades for human and mechanical units. Upgrades improve the stats of your units (including workers!) like damage, armor and speed.

Upgrades
Humans

Attack: 

Armor: 

Speed: 

Mech

Attack: 

Armor: 

Speed: 

Strength
Forges are not powerful by themselves, but the ability to give you powerful defensive & offensive upgrades are a vital tool for winning longer games or establishing a timing attack!

They are also at the bottom of the tech tree, allowing for quick research at minimal investment as the forge is only 150g!

Weakness
Forges rely on other units and buildings to be effective and can open you up to attack if your opponent realises you are low on either economy or units due to the investment.

Forges can also give away your strategy if they are scouted, so be sure to keep them hidden!

Strategy
Doubling your research rate

If you got the gold for it, then building two forges is really recommended. All forges of the same player can upgrade the same thing at once, and they don't even have to be done to research the next level. To explain the last sentence, when you appoint Forge A to research Armor 1, you can already appoint Forge B (if you have it) to research Armor 2. This really speeds up research and you can get an edge in combat because of the faster rate of upgrades your units are getting.

Don't forget that it upgrades your workers as well, which means a fully upgraded (+5/+5) worker is about the same as an un-upgraded soldier! Imagine an army of mineral walking upgraded workers!

Development
1.94: Human upgrades: increased duration from 100 (+10) to 100 (+20)