Research

Updated for 2.0!
In 9/10 cities I conquered I had to reset some research in the academy wasting my Culture Points. Its amazing how many useless technologies people have in their cities! I will give a brief description of all of them and will tell you on which you should never waste your points. All technologies help more or less but since we cant have them all in one city then its important to prioritize them and to have really important ones.

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I found out that in most of my cities I have almost the same set of technologies no matter what is the specialisation of a city. So I want to make a list of things we should always have and which to avoid in every polis.

As a basic rule, always have researched technologies which provide extra firepower and speed of production. Then you can focus on costs and movement speed.

All technologies help more or less but its important to prioritize them. For example Meteorology wont help you if 99% of your enemies are based on other islands (usually are, except very early stage of the game).

Must Have Techs

Farm Spaces (army size):

• Plow - instantaneously receive 200 citizens, every extra FS is good

Firepower:

• Phalanx - MUST, your troops fight 10% stronger than normal
• Battering Ram - MUST, the fighting power of your ships increases by 10%

Resources:

• Booty  before 2.0 - your units carry 30% more resources
• Booty after 2.0 - With this researched, it will give you 4 more options of looting and demanding. I dont think they are that good for looting (default ones are good enough), however they give you extra flexibility in Demanding tab. Now you can Demand every 10, 40, 180 and 480 min. Of course default  option to demand every 5 min gives the most resources but who has time for it? 2x10min will give more than 20 min option, 2x40 more than 90. However the most important is 480imn option, as it is 8 hours total, which is long enough for a healthy sleep ;) 240 was to short and we cant loot each night.

• Horsemen - great farmers and offensive units
• Ceramics - warehouse can store an additional 2500 resources, spillage is bad

Navy:

• Shipwright - speed of production is important and you will produce boats in all types of cities

0 points (so why not if you can afford it to have in every city for even fake attacks purpose)

• Conquest - must have to conquer another players city and make it yours
• Colony Ship

Sometimes, depends on specialisation 

Land army city

• Trainer - essential, your barracks work 10% faster, to fast rebuild your troops
• Light Transport Boat - excellent, must have for quick attacks and support (read more here)
• Bunks - transport ships can carry 26 units instead of 20 and fast boats 16 instead of 10

typical defensive

• Archers - to farm villages (before 2.0) and excellent defensive

typical offensive

• Slingers - excellent offensive (def city doesn't need slings)
• Conscription - good for assault cities, cost of land units reduced by 10%
• Catapults - very useful, mix with land nukes (read more here)
• Breakthrough - for land nuke cities its a must (read more here)

Naval cities

• Biremes - essential for naval defense
• Lightship - essential offensive and for escorting transport ships
• Mathematics - costs for ships are reduced by 10%
• Cartography - 10% faster ships 
• City Guard - increases your militia, is good as it increases the amount of damage you deal if you dodge an  attack. Not bad to have in offensive or pure naval cities.

Conquest City

• Chariots - only useful for conquering forces mixed with hoplites or Cyclops
• Trireme - the same as chariots
• Hoplites - for colonising, sharp attack or blunt defense

Other

• Fireships - if you want to change a city into a defensive fort, but moving them around is pain in a... There used to be a trick (maybe still is) that sending 1 fire ships with your CS would save it in case of wipe. You see, Fire Ships in battle mechanics fight before CS but they cant be sunk when they are attacking (they can only be sunk when being attacked by LS). Therefore If your CS wave would wipe, then at least your CS could come back home.

• Diplomacy before 2.0 - dont trust it 100%. Without diplomacy researched, the chance of a revolting farming village starts at 75% mood, with diplomacy researched this becomes 60%. So you can farm away till 60% with no risk of losing your units. But, this way you cannot farm every farming village more times a day because the mood increases at the same speed as before. Instead, you can farm more resources in a short period with longer delays (nights) between these periods. When I played I never had problem with that but for some people who log in less often it might be useful rsearch.
  
• Diplomacy after 2.0 - In 2.0, it will allow you to loot to 64% mood without fear of revolt, instead of 80%. If you really cant log in often enough to farm resources or have to many cities to look for its ok to take it.

Useless techs (in the advanced stage of the game)

Some of these technologies MIGHT be helpful in the very early stage of the game, but can you afford to reset them later on?

• Architecture - resource cost of buildings lowered by 10% in the early stage it can help
• Crane - increases building speed in Senate by 10%
• Demand Troops - it saves time to produce units but its a lottery what you get, pretty useless. After 2.0 the demand troops research was removed from the tech tree. In all worlds with 2.0 or higher implemented, the demand troops option for farming is available automatically after you upgrade the village to level 3.
• Meteorology - its a joke, maybe useful in the first couple of weeks of game

Absolutely worthless techs:

• Cryptography - put some silver in your cave instead
• Democracy - yeah right, like if these extra 2 hours gonna save you
• Espionage - Spies travel 10% faster...eee how does it help? you want reports quicker? send them before. Well maybe in Heros world it might be used for many quick spy missions and time is essential there.

If you have any doubts or questions post a comment. I encourage you to debate :)