Fame Points are awarded when characters have attained offices, performed certain actions, or achieved certain statuses. Each Fame Point is unique, and will be given only once for each condition fulfilled. Trying to trigger the events with another character will not grant you repeated Fame Points, as it is a family attribute.
Many fame points are also granted after a short delay or on the turns. For example, if you get appointed as a region lord and step down immediately, chances are that you won't get the fame point for holding a local lord position.
While the majority of the Fame Points have been discovered, there are still a few that remain unknown, as Tom wishes to leave it that way. This page outlines all of the known Fame Points. The speculation page on the possible, undiscovered Fame Points is referred to as Lemon Fame. The other page features some stricter tested guesses is referred to as Fame Box.
(12 known points)
- You will get 1 point each for being elected or appointed to any of the 4 council positions (Ruler, General, Judge and Banker). (very small realms do not grant these fame points)
- Rulers will also get 4 points on their 10th day (provided the realm has 5 or more regions) and 1 point for the 100th day of consecutive rulership (even one day of interruption will reset the counter).
- Being appointed as a Region Lord will get you 1 point, while being appointed Duke will get you 2 points. This means you can get 3 total for being first lord of a, say rural region and then lord of a city.
(8 known points)
- Fame is granted for high prestige of individual characters, namely 1 point each for reaching 10, 20 and 40 prestige.
- Fame is also granted for high sum of prestige across all characters, namely 1 point each for reaching a sum of 20, 50 and 100 prestige.
- Wealthy families can also get 1 point each for reaching 2000 and 5000 gold.
- 1 point is awarded when any skill reaches 50%.
(11 known points)
- 1 point for publishing a book (requires Mentor points)
- 1 point for acquiring a total of 50 mentor points
- 1 point for Building a Palace or Moving the Capital
- 2 points for founding a guild or religious order
- 1 point for making a Family Investment
- 3 points for winning a tournament
- 1 point for hosting a "successful" tournament (note)
- 1 point for feeding a starving region
(6 known points)
- 1 point for being killed as a non-hero (usually by execution)
- 1 point for winning a Duel to the death, only if the loser actually dies
- 1 point for dying as a hero
- 3 points for dying as a "legendary" hero (this is a 2nd death, so to get all 4 points, you will have to lose two heroes, one legendary and one non-legendary)
These are fame points that are known and have been confirmed by Tom, but details are still missing so that they are not included in the list above - (at least 3 known points)
- There is at least one point of fame for skill(s).
- Being the Founder of successful religion grants fame in addition to founding it. How much and what the criteria for "successful" are, nobody but Tom knows.
- Sponsoring a successful army (must found the army as well, having sponsorship transferred, i.e. death of its sponsor while you are ruler, will not give you the point).
- What exactly is a "successful tournament" ?
Since many players enjoy speculating about the unknown fame points, here are some hints on the unknown Fame Points, from Tom himself:
- Only one Fame Point has not yet been collected - all other Fame Points have been earned by at least one, usually many. This one un-discovered Fame Point can be earned in battle.
- There is Fame in religion
- There is Fame for exceptional skill(s)
- There is a Fame Point that can be gained in the infiltrator career (technically also in others, but Tom doubts anyone but an infiltrator could really pull it off). It's not based on Honour, though. 
- Some of the recently added Fame is easier for non-addicts to achieve, so some of the lower families will get Fame, too. 
- There are some exceptions to the above points for adventurer characters
(Note that the above hints predate the 2007/04/25 update to 51 Fame points. Presumably, the brand new point is from a new feature that was added at the same time, and has probably not yet been achieved.)