As Armin Saberlin said in pre-searing Ascalon: "There is no right or wrong choice. Every combination of professions has unique benefits and possibilities."
This is, however, one of the most common questions asked. So here are some quick benefits to each secondary profession (arranged alphabetically). (Note that this was created before the introduction of the Sunspear and Faction PvE skills, I'll add that information later.)
Using daggers with Avatar of Lyssa and Heart of Fury, shadow stepping, melee interrupts.
Conjure <element> combines with elemental scythe damage, enchantments that increase armor rating, wards, and glyphs for energy management.
Hex removal and prevention (i.e., Hex Breaker), stances to reduce damage, energy maintenance, skills such as Epidemic to spread conditions, Illusionary Weaponry [E].
Reusable resurrection spells, condition removal, a number of Protection Prayers enchantments which can help with Dervish skills like Mystic Sweep or Mystic Regeneration.
Plague touch for condition removal (works well with Wearying Strike), Orders spells and curses such as Barbs or Mark of Pain.
Shouts, echoes and chants, specifically "Go for the Eyes!" to increase damage or Soldier's Fury [E] to increase attack speed. Reusable resurrect skill, condition removal signets.
Pets, skills such as Apply Poison, stances, Antidote Signet to remove conditions.
Weapon spells (notably Splinter Weapon), reusable resurrection spells, condition removal.
Defensive stances, shouts. Wild Blow and melee interrupts.
This synopsis was compiled from multiple threads in this forum, but if you have additional notes, I will update this post.