The direct descendant of Classic Heavy Metal (eg. Iron Maiden) is Power metal.  While bands such as Iron Maiden and Judas Priest are technically Power metal, they are old so I will consider them Classic. 
Power metal is characterized by upbeat tempos and energizing and catchy songs.  Rhythm guitars here are fast powerchords, heavy, but not downtuned.  While the lead guitar is usually wailing solos and accelerated classical scales.  Drumming quite often employes thunderous double-bass and high speed beats.
Power metal vocals are clean, soaring and high-pitched, often operatic at times. Lyrics in this genre are generally uplifting and triumphant, often giving the listener a sense of euphoria.
Many Power metal bands write lyrics dealing with medieval fantasy: dragons, warriors, wizards etc.  To some these lyrics can seem cheesy and can be a turn-off, but to a fan, it is just another part of the fun of Power metal.
It is very common for Power metal bands to integrate epic symphony pieces into their songs to give an extra-powerful sound.
I RECOMMEND:

Above all else
RHAPSODY. Click on the name to see more about them.
On to the others...

The creators of modern power metal: HELLOWEEN.
These guys created the 'happy' sound that bands like Rhapsody use today.  They deserve credit for inspiring so many great bands, and their music is excellent too.  High pitched, clean vocals.
I'm not a real expert on HELLOWEEN, but I know everyone should listen to the albums
Keeper of the Seven Keys: Part I and II.
Future World, I'm Alive and Twilight of the Gods are each a good listen.

FREEDOM CALL
One of the first Power metal bands I discovered.  Their music is so uplifting and often deals with God, heaven, angels etc.  Their singer is amazingly high pitched (but great.  The only negative?  Their synthesized brass instruments sounds really, REALLY fake sometimes, but that doesn't subtract much from my enjoyment.
All their albums are excellent, so I say start with the first:
Stairway to Fairyland, but ensure you get the others too.

BLIND GUARDIAN
These guys have been around a while now.  (Compared to Freedom Call, Rhapsody etc)  They play a harsher type of power metal.  Their earlier albums were pure power metal, but they have become more and more symphonic over time (not a bad thing in my opinion).  High but a bit rough vocals.  Did a whole album about Tolkien's Silmarillion!  And it rocks!
My favorites: 
Imaginations from the Other Side, Nightfall in Middle Earth, A Night at the Opera.
 
EDGUY
Excellent power metal!  Classic high, clean vocals and really catchy riffs with frequent symphonic elements.
They should be noted for creativity in their lyrical content, as its not just typical fantasy power metal.
I like: 
Vain Glory Opera, Mandrake

DREAM EVIL
Rather new band on the scene.  They have mixed classic power metal and the modern kind together. The result is a pleasing, heavy and aggresive sound.  Not much in the way of orchestral arrangements here (on a few ballads, thats all) just blasting guitars and drums.  And of course killer vocals.
Their first album,
Dragonslayer, is a fantasy story.  Sure it's typical fantasy fare, but the music is great.  While not as great as the first, the 2nd release, Evilized, is pretty good too.

HAMMERFALL
German power metal that stays rooted in old-school style.  Somehow these guys manage to keep their music interesting without employing symphonic elements.  One of my favorite singers.  Their pumping rythyms will get you ready for battle!
The legendary
Legacy of Kings, followed by the new Crimson Thunder, are my choices.

SONATA ARCTICA
A bunch of younger guys from Finland, they have a distinctive sound that relies heavily on keyboards.  Very melodic stuff.  Their singer is super-high pitched at some times.  Hard to describe, you must hear it yourself.
I own only
Ecliptica, but I have heard some of Silence and both are excellent!

STRATOVARIUS
Considered legends by many, I personally don't think they are that great. 
Visions is supposed one of their best, but I would call it 'good' at most.