Skill point

Skill points are points awarded to the player character when reaching a new level of experience. The player is then free to allocate the points to whatever skills they feel are in need of improvement.

Certain books, traits and perks give the player a skill point bonus for a specific skill as well.

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

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

The number of attainable skill points (without books, and not including what your skills are at character creation or your tagged skills) is 428. Combined with the Comprehension perk and every Vault-Tec bobblehead, you can achieve a 100% stat in all 13 skills, though it might take some time searching the wasteland for everything.

An INT of 10 means 20 skill points per level-up, making INT a very useful skill.

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 to divide amongst all your skills.

Fallout: New Vegas
Skill points are earned when reaching a new level of experience. Intelligence is the determining factor on how many points you receive. Points = 10 + (INT/2).

Note that 0.5's on odd intelligence level gains are saved for the next level. Example: You have 9 intelligence. First level up nets 14 points. You level again and net 15 points. In reality you gain 14.5 then 14.5, but obviously the game cannot allow you to increase a skill by 1/2.

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.(Addons increase level-cap, further increasing the amount of extra skill points by 10 per add-on).

Maximum points
The maximum obtainable amount of skill points (without add-ons) is 489. This requires creating a character with 9 INT, taking the Educated perk at level 4, and getting the Intelligence Implant (requiring 4000 caps) before reaching level 2. An alternative is to just create a character with 10 INT. This is not recommended due to the availability of implants. It's worth noting that the difference of getting the implant sooner rather than later is of only a couple points. Getting the implant at level 9 will get you a total of 485 points. Even getting it at level 25 gets you a total of 477, only 12 short of the max. This is roughly equivalent to an extra level-up's worth of skill points if you had an average INT level. With the DLC's extra 20 levels, there is a maximum of 829 points available (Educated perk at level 4)