What are the most beneficial ways to use experience boosters?

I've recently purchased a digital copy of Guild Wars 2 that came with 10 experience boosters. Those grant 50% bonus experience for one hour straight. How to make good use of this bonus and maximise the amount of experience earned ? (i.e. Are there any quests that I should use those on ?)

It's actually worth reading the fine print on those (from the wiki, emphasis added):

Double click to gain a buff that gives an additional 50% experience from kills for one hour.

GW2 doesn't really have "quests" as such, and while there are many, many things that will give you experience (from ressing people to crafting to completing renown hearts to mining and so on), the booster won't help you there; it is most useful for going out and, well, killing stuff.

The most efficient way to do that is probably doing PvE event chains or WvW events with lots of other people, and learning to tag - the more people there are, the more a PvE event scales up, and (at least in the case where multiple mobs are involved, not just one boss) that means more mobs. Hit as many as you can at least once, then switch targets, or use AoE skills that will tag multiple targets for you. Each time you contribute to a kill, you'll get experience, and the booster can do its work. Best for this are probably events where you have to defend against multiple waves of foes, as getting many WvW kills can be difficult until you get the necessary experience (and have a good WvW server).

With the recent changes to dailies, there is usually one area (zone) where people go for daily events, meaning events scale up more. Sadly, all too often the scaling in low-level areas doesn't keep up with numbers and it can be difficult to tag anything before everything around the event is dead because of the number of overpowered players. If you have a level 80 character, I'd recommend going down to Orr and doing event chains there, such as Plinx or the temple events, but unless you're desperately in need of skill points, that's wasting the boosters to some extent - personally, I'd try to use boosters on characters I'm levelling up to get to 80 quicker. I've lost count of how many Exp boosters are sitting in my account stash, unused.

By the way, if it wasn't clear, that one hour is while that character is logged in, so logging off or switching alts doesn't use up that timer. And... welcome to GW2 :-)

Personally, I don't find the XP Boosters to be all that useful, because they're from kills only. What I would do is obtain some Boost Enchantment Powder. These will turn those boosters into an Enchanted Reward Boost which will let you select from a menu of boosts. Of course, you can't do this right off the bat because 10 powders costs 1 gold.

Amos is right on. I find the biggest benefit from them is in converting them to something else, especially when you already have an 80. You can turn them (and most boosters) into a generic booster that can be then converted into something you might find more useful (crafting is usually my preference) by buying dust from one of the vendors that is located nearby the black lion NPCs. I think that the dust is fairly cheap, and it makes it a lot easier to store them when you get a bunch of different types of boosters as you play. Welcome to GW2!