Luck is an Attribute that affects everything you do in a small way, from attacking, to the chance of successfully enchanting an item.
Luck is special in that it is not the governing attribute for any particular skill. Thus, Luck never receives a bonus multiplier when you level up, and can only increase +1 per level. Most effects from good Luck can be achieved by trial and error with use of quick saves, but a high Luck is quite handy in many situations, including lock picking and alchemy. If you choose to never increase your Luck in level-ups, you might want to create a Fortify Luck spell, enchantment, or potion for those occasions when you need to be extra lucky.
Luck is very important for mages, because it increases the chance to successfully cast spells. In Morrowind, spells can be created that have a chance of 0% of being successfully cast even if one has mastered the necessary skill. But with enough Luck one can increase the casting chance to any number.
Luck, however, has no effect on the quality or quantity of random loot that you find. This is an old myth that has been proven to be false.
All characters start out with 40 points in Luck, regardless of race, gender, class, or birthsign; unless they have Luck as a favored attribute (only possible on custom classes), in which case it is 50.
It is possible to max out the luck attribute by level 51 (if luck is a favored attribute, otherwise level 61) by sinking a point into it at every level up. As it can only be increased by 1 each level, it's best to start as early as possible if 100 Luck is a goal for the current character. (While it can be achieved at an even earlier level with the Bitter Cup, this can only be done at the cost of a valuable quest reward and only with Luck as one's highest-raised attribute at the time of use.)
- 100 luck can be obtained at level 31 if you have Luck as a favored attribute and use the Bittercup.
- The Siege at Firemoth official plug-in adds an artifact called the Ward of Akavir, which has a constant effect enchantment which increases Luck by 25 points.
- A creature with 100 luck is the last living Dwemer, Yagrum Bagarn (he must have been very lucky to survive). This makes it hard to hit him with attacks or spells.
- If you have Tribunal installed, you can see the effect of Luck in combat while fighting a certain Bosmer. Gaenor's unusually high luck of 770 in addition to his level and high armor rating makes him very hard to hit.