What are the Magic Combos in Dragon Age: Origins?

One of the loading screens mentions that there are some extra strong magic combos.

So what are those combinations and what is their effect?

Are there also special combos for warrior/rogue-skills?

Solution 1:

Spell Combination                                     Result

Grease + Any Fire Spell                               Grease Fire
Death Hex + Death Cloud                               Entropic Death
Glyph of Paralysis + Glyph of Replusion               Paralysis Explosion
Spell Might + Blizzard + Tempest                      Storm of the Century
Grease Fire + Blizzard                                Flame-Quencher
Force Field + Crushing Prison                         Shockwave
Vulnerability Hex + Drain Life/Mana Drain             Improved Drain
Spell Might + Animate Dead                            Advanced Reanimation
Sleep + Horror                                        Nightmare

• Grease Fire: Burns for 30 fire dmg/1.5sec for 20 sec, friendly fire
• Entropic Death:: Targets with Death Hex entering Death Cloud instantly suffer 200+2.0Xcaster's spellpower spirit damage
• Paralysis Explosion: All targets withing 7.5m are paralyzed for 20secXtarget rank
• Storm of the Century: Caster loses additional 100 mana, causes (30+0.3XSpellpower) electricity damage every 2 sec for 30 sec and drains Stamina equal to damage dealt, friendly fire
• Flame-Quencher: Puts out a Grease Fire
• Shockwave: Knocks down nearby targets and causes 50+0.5XSpellpower physical damage, friendly fire
• Improved Drain: Drain Life deals 100% more damage to enemy and 100% more healing to caster, while Mana Drain steals 50% more mana
• Advanced Reanimation: A skeleton minion at 0.9Xthe caster's level with additional abilities is summoned
• Nightmare: Removes Sleep, applies Horror, then causes 100+1.0XSpellpower instant spirit damage

This one's slightly different, but in the same vein: Hit a target that is Petrified/Frozen, then get a Critical Hit or use Stone Fist/Crushing Prison and they will Shatter, which is an instant kill.

Source

In regards to your bonus question, no, there's not really an equivalent functionality with warrior/rogue talents. There are tactical synergy options, like having your melee characters hit frozen/petrified targets to one-shot them. Rogues also get a Coup de Grace talent which does additional damage against stunned/paralyzed targets, so you could send them after enemies your mage mezzes. But there are not really "combos" in the same way that the mage spells work.

Solution 2:

It's Spell Combinations, the wiki at the link lists exactly how to get each one.