Lately, we've talked quite a bit about how and where to find various timed quizzes. Of course, once you find them and try them out, the next step is getting better at them!
I can't help you out with every quiz, but many of the topics have been around long enough that several well-known mnemonics have been created for them.
Sporcle's recent addition of the Planets quiz is a good example. Fortunately, they've included Pluto in their planet quiz, so my favorite older mnemonic will work. While there are numerous planet mnemonics, I've always favored My Very Easy Method Just Speeds Up Naming Planets. Some people do get confused between Mars and Mercury, however, I've always remembered that Mercury is closer to the sun by thinking of the mercury in a thermometer, and thinking that the mercury on Mercury is much too high.
Moving in on Earth specifically, how about something that seems really tough, like Mogroware's Geological Time Periods quiz? The phrase Camels Often Sit Down Carefully; Perhaps Their Joints Creak? Persistent Early Oiling Might Prevent Permanent Rheumatism can help, as explained here and here. Some people add Pregnant at the beginning to remember Pre-Cambrian, and others replace Rheumatism with Hurting, in order to remember that the recent period is also known as the Holocene period. In the geological time periods quiz, they also include Mississippian and Pennsylvanian periods, but since these are both named after states, they're easily remembered.
Speaking of history, the answers to the Shakespeare's Plays quiz can be learned by reading my posts on mnemonics for the histories, the tragedies, and the comedies. You may also want to read the comments of the comedies post for another excellent Shakespearean mnemonic method!
I was pleased to see a Taxonomic ranks quiz, as this has been a rich area for mnemonics. While you can find plenty of taxonomic mnemonics here and here, the one I've always used is, Do Kids Playing Constantly On Freeways Get Squished? The Do is used to remember domain, while the rest apply to the standard order.
While Kongregate, Mental Floss and Sporcle all feature quizzes on the elements, this is a long list and isn't easy to remember. The few people who can name the majority of the elements have usually put in the time to learn Tom Lehrer's classic elements song:
For quizzes on the western zodiac, like the ones at Mental Floss and Sporcle, there are several approaches here, including a couple of handy poems. If you're trying to remember the animals of the Chinese zodiac, however, there's an ingeniously simple mnemonic you can use.
Because religion is central to so many lives, it's not surprising that there are numerous Bible-themed timed quizzes, nor is it surprising that so many mnemonics have developed to help people remember these lists. The twelve apostles/disciples can be remembered with this poem, as well as these other memory aids. Being short lists, the Seven Deadly Sins and the Plagues of Egypt can be learned quickly (The Exodus Decoded documentary can also help you remember the plagues).
The first 10 rules that God spoke to Moses on the mountain, often mistakenly called the Ten Commandments (The list on Moses' stone tablets, which is specifically referred to in the Bible as the Ten Commandments, is in Exodus 34, and not in Exodus 20), have a reputation for being hard to learn, but the following video is among the quickest ways of learning them:
Probably the toughest of the Biblical memory challenges, aside from remembering any version of the Bible word-for-word, would be naming all the books of the Old (OT) and New Testaments (NT). The earliest ways of remembering these included finger methods, poems (OT only) and songs. As aids like the Major/Peg system developed, these were used to remember all the Bible books. Computers can help greatly, as this Bible book location game shows (turn off the flashing background, the directional arrows, and the section highlighting for a real challenge).
Any of the numerous flashcard programs on the web can be a great help on any of the subjects you wish to learn. If you're looking for established mnemonics (or ideas for new timed quizzes, for that matter), sites such as Memoria Technica and Amanda's Mnemonic Page can also be of great help.