There is a mirror listed in the DMG under Goods and Services; it has no listed mechanics, which is already a bad sign. Additionally, Dungeonscape does not consider a mirror to be useful dungeon-delving gear, since it fails to mention it.
Rays and spells in general: No
Line of sight does not say anything about mirrors.
To determine line of sight, pick any corner of your space and trace a line from that corner to every corner of the target's space. If at least one line doesn't pass through or touch an object or effect, then you have line of sight.
For spells, you're also boned by the Line of Effect rule.
A line of effect is canceled by a solid barrier.
Despite being shiny, a mirror is a solid barrier. So no, you could not bounce a ray off a mirror to have it affect a creature that you don't have LoS or LoE to.
Gaze: No
Gaze attacks explicitly don't work with reflections. From the description of the "Gaze Attacks" special ability:
Looking at the creature's image (such as in a mirror or as part of an illusion) does not subject the viewer to a gaze attack.
There is one explicit exception to that rule, the Thought Slayer's Mind Consuming Gaze:
If a thought slayer’s gaze is met indirectly (such as through a mirror or a reflection in water), the opponent does not die on a failed save but instead is dazed for 14 rounds.
Illusions: Probably
Illusions also do not mention mirrors. However, it makes sense that an illusion would reflect in a mirror, since you are still looking at it (albeit not directly). Defeating the entire school of Illusion with a 10gp mirror would be very sad indeed.
Special vision: Depends on the spell
Different vision spells have different rules. For example, see invisibility works "within your range of vision" so a mirror would definitely work. However, aura sight needs subjects to be within Line of Sight to work 100%:
The owner of each aura is revealed, unless the individual is outside your line of sight.
There is a similar clause in arcane sight:
If the items or creatures bearing the auras are in line of sight, you can make Spellcraft skill checks to determine the school of magic involved in each.