Paladin

Protection

Strengths

• You can heal yourself.
• You have the best armor in the game.
• You have AoE, targeted spells, and good melee.
• AoE Farming If you are pulling a big mob, you can take it down with AoE, while healing yourself.
• The Paladin "Bubble" will save you from near death, and you can also hearth back home or heal yourself.

Weaknesses

• None! Paladins have amazing buffs and heals, making them almost immune to damage, and that is topped by their armor efficiency.

If you want me to go deeper into why a Paladin is easiest to level, just comment.

Rogue

Combat

Talent Spec: 13/53/5

Strengths

• Can Stealth past mobs for gather quests.
• Can CC mobs to kill larger groups
• Can vanish away from bad pulls/gankers
• Can eventually solo group quests (takes more skill than most classes to do it but skill doable)
• Flexible with weapon choices (Hack and Slash can be switched to weapon of choice)
• Stuns :D

Weaknesses

• Dies a lot if you aren't great with the class
• Uses leather so is relatively squishy to most melee mobs
• Has buggy mechanics (Vanish is nothing close to reliable, although this may be unnoticeable while leveling)
• Has no AoE until level 80 (Blade Flurry still hits multiple targets but isn't technically an AoE.)
• Long dungeon queues as a pure class
• Only group buff is Savage Combat

Glyphs: Sinister Strike / Eviscerate / Slice and Dice / Blurred Speed / Vanish / Safe Fall and switch one of the majors out for Killing Spree at level 60.

Provided Recruit-a-friend is still going on, any class is easy to level when you share triple experience with a buddy. To get the benefit of a speedy trip to level 60, you must be within 5 levels of each other, and close to each other during playtime. If you have done the recruiting, and are leveling an alt, this is a great way to connect with someone, as well as use your heirloom gear. Your recruit can also grant your alts levels as well, skipping the leveling process, but adding training costs.

I have 9 lvl 80 characters myself, and by far the easiest time I had leveling was:

Death Knight

Suggested Spec: Blood Tank

Pros

1. Self healing: Through specing properly in the blood tree not only will 4% of your damage done be returned to you in heals, you will heal yourself for 10% of your max HP ( assuming you have IT and PS up ) with your Death Strike.

2. Durable: With a solid tank set full of defense and stamina, and taking into account point 1 above, you will find you can solo 'most' group quests with relative ease. I found I could handle any group quest that suggested 3 players.

3. Quick dungeon queues: As you get burnt out a bit on the quest grind, the queues for a tank are often less than a few minutes.

Cons

1. While the healing is powerful, it's easy to not pay attention to your runes when fighting 9+ mobs, spend the death runes you have on hard hitting blood boils or heart strikes and not have anything up for a Death Strike to heal yourself.

2. Diffucult to gear as a tank. Until Northerend content true 'tank' gear is difficult to find. I see many DKs go into a random instance in BC content with full DPS gear and straining the healer as they try to tank.

3. No 'good' snap aggro. Blood boil may be the best 'oh crap..' snap aggro ability available. However it's damage is dependant on a disease being present on the target being afflicted, as such wont do near as much damage, thus threat, as you may expect. DnD is great, but for that 'oh crap..' situation listed above often times DnD is going to be on CD or you won't have the runes for it. In addition it needs the mob to be in the AoE for a second or two to tick the damage in for the threat.