Skill point

Skill points are points awarded to the player character when reaching a new level of experience. The points can then be allocated to whatever skills they feel are in need of improvement. Certain books, traits, and perks give the player character a skill point bonus for a specific skill as well.

Fallout 1 and Fallout 2
$$\text{Skill points per level-up}=5+(2\times\text{Intelligence})$$

Fallout 3
$$\text{Skill points per level-up}=10+\text{Intelligence}$$

The number of attainable skill points (without books, and not including what the skills are during character creation or tagged skills) is 428. Combined with the Comprehension perk and every Vault-Tec bobblehead, one can achieve a 100% stat in all 13 skills.

An Intelligence of 10 means 20 skill points per level-up, making it a useful SPECIAL stat for receiving skill points.

The Broken Steel add-on raises the level cap to 30, and therefore adds a potential 230 extra skill points to the game, for a total of 658 skill points.

Fallout: New Vegas
Skill points are earned when reaching a new level of experience. Intelligence is the determining factor on the number of skill points received.

$$\text{Skill points per level-up} = 10 + \frac{\text{Intelligence}}{2}$$

Note that 0.5's on odd Intelligence level gains are saved for the next level. For example, with 9 Intelligence, the first level up nets 14 points. The next level up will net 15 points. In reality, the player character gains 14.5 points then 14.5 points.

Skill books will also permanently increase skills.

The perk Educated, available at level 4, adds an extra 2 points per level up. This yields an extra 52 points if taken at level 4. Add-ons increase level-cap, further increasing the number of extra skill points by 10 per add-on.

Maximum points
The maximum obtainable amount of skill points (without add-ons) is 502. This requires creating a character with 10 Intelligence and taking the Educated perk at level 4. It is also possible to get the maximum skill points with a starting Intelligence of 9, by getting the Intense Training perk or Intelligence Implant before reaching level 3. With the add-ons' extra 20 levels, there is a maximum of 827 points available. Also through the use of an exploit involving the Skilled trait and Intelligence of seven or eight, it is possible to gain 100 in every skill by levels in the upper 40s (this still requires most skill books, but does not require the Comprehension perk).