Does content scale with level?
In Diablo 3, do the mobs that you face in the world and dungeons scale to meet your level?
For example, without taking skills gained during levelling into account, would a Level 8 character breeze through something that a level 5 character may struggle on?
Yes!
All content scales with the level of the character that created the game. This changed in patch 2.0 (the pre-Reaper of Souls content patch).
This patch replaced the existing difficulty system (which did not scale) with a "Monster Power" style difficulty system. This means that as the game host levels up, the overall difficulty of the game rescales to the new level.
This is further clarified by Grimiku, one of the community managers at Blizzard:
So, the Normal > Nightmare > Hell > Inferno progression path is gone. Instead, starting in the pre-expansion patch, you’ll find that monsters will level up as you do, and they’ll gain additional affixes depending on what level range they’re in. You’ll be able to influence monster damage, health, and rewards by selecting one of nine new difficulty settings* as well, similar to the way Monster Power works currently. The result is that you should have a lot more freedom in customizing your level of challenge without worrying about multiple playthroughs of the story to get there.
As of 2.0 / Reaper of Souls, enemies now scale to your level everywhere in the game (but they are still stronger on harder difficulties).
No. The level of the monsters are fixed based on the difficulty level (normal, nightmare, hell and inferno) and your progress through the various Acts.
If you are having problems with a difficult boss, you can grind some experience, gain a few levels, and the encounter should be a bit easier (although better gear, either from drops, or bought from the AH, will generally provide more of a benefit than levels unless you are missing a key skill/rune).
This is especially important in Hardcore mode, where it is better to be a few levels higher than normal for boss encounters.