Alerts [2000/day + 1 questionite box / nemesis alert]
By Defender in Millenium City's Rennaisance Center is Lt. Patil. Every day, he will give you one mission for doing three regular Alerts, which will award 2000 Questionite for the set. The only difficult thing about these Alerts is getting enough people to queue for them.

Alerts can be requested and turned in through your Crime Computer, listed as 'Alerts Coordinator', so you don't have to leave whatever zone you're in to get these rewards.

Additionally, nemesis Alerts always award one Questionite crate. Combined with the credit towards rare Perks, it's always worth clearing a nemesis Alert.

Rampage [1500-4500/day]
Rampage is a special alert type that awards Questionite, available starting at level 35. The first time you complete it each day, it's worth 1500 Questionite, but every subsequent time you repeat the Rampage within 24 hours, the reward drops by 300; this means that you can do a Rampage alert five times for a maximum of 4500 Questionite every day. Rampages tend to be a bit more difficult, but once you've done it once for 1500 Questionite, you can repeat it right away.

The type of Rampage available changes every Friday. Some are incredibly fun (Lemurian Invasion), while some require coordinated effort to complete (Fire and Ice).

If you're facing a rampage that isn't worth doing (Gravitar, Fire & Ice), these can also be used to earn Questionite - not as fast as an alert, but far more fun than the broken rampages.

Aftershock [2000-8000/day]
Aftershock is an Adventure Pack, a series of five missions available from level 11 UNTIL Liason Bradley near Defender in Millenium City's Rennaisance Center. It can be repeated up to four times per day, but each run requires about an hour.

Crisis in Lemuria [1500/day]
Starting from level 34. Once per day, you can get an instance of the Lemurian crisis from the Drifter in Rencen, shoot fish in a barrel, and get 1500 questionite. This is probably the fastest questionite-per-minute mission in the game (including the three alerts), taking 15 minutes tops to clear the four sections and netting you credit towards some rare perks, but the trick is getting a team of five people together who are willing to do it.

Crisis on Monster Island [1500/day]
Starting from level 30. Once per day, you can go to the Drifter in Rennaissance Center and get a special instance of Crisis on Monster Island. It's incredibly fun to blast through with a group, but upgraded travel powers are suggested.

FATAL ERR0R [1000/day]
Two quick missions each give 500 Questionite; additionally, the first mission awards credit towards a rare Perk you can't get elsewhere. However, the big bug battle at the end of the first mission really requires at least one tank. Socrates hands these missions out, and can be found in the Crime Computer.

Technically, this is your first chance to earn Questionite, seeing as this mission is available from level 6, but you'll definately want a full team or to be part of a much higher level team if you do this.

Nemesis Confrontation [3-6 questionite boxes/run]
The Nemesis confrontation, available at level 40 and once you've done some missions versus your Nemesis, awards credit towards some unique Perks as well as 3-6 Questionite boxes: one from each Nemesis, and one from the big boss at the end. This awards on average 1000 quesionite/run.

Operation Demonflame [2000-8000/day]
Operation Demonflame is a 'Comic Series', a series of five missions available from Major Violette Boudreau in Millenium City's UNTIL headquarters (just southeast of Rencen). It can be repeated up to four times per day, but each run requires about an hour.

Resistance [2000-8000/day + 1-2 questionite boxes/run]
Resistance is a 'Comic Series', a series of missions available from Defender in Millenium City's Rennaisance Center, against a superfluous amount of Destroids and Karakadon, as well as the only reliable credit towards the Prison Guard defeat perk. You can use vehicles for the first few sections, as well, which maximizes the Gravity Pulse Fun Time you can have streetsweeping. It can be repeated up to four times per day, but each run requires two to three hours - more if your team tries to use 'clever' expoits to avoid fights.

Serpent Lantern [2000-8000/day + 3-5 questionite boxes/run]
Serpent Lantern is a 'Comic Series', a series of five missions available from Major Kwame in Millenium City's UNTIL headquarters (just southeast of Rencen). It can be repeated up to four times per day, but each run requires about an hour. The sheer number of VIPER supervillains you fight will definately cause your earned Questionite to go above the listed 2000.

Whiteout [2000-8000/day]
Whiteout is a 'Comic Series', a series of five missions available from Defender in Millenium City's Rennaisance Center. It can be repeated up to four times per day, but each run requires about an hour. It involves a lot of running around the great Canadian north, so having upgraded travel powers is recommended.

Alerts: Vigilance [special]
Of special note is the mission Alerts: Vigilance, from Lt. Patil. It can award up to 50,000 Questionite... but only once every seven weeks, by completing each weekly custom alert. It doesn't replace the daily grind, but having the extra bit certainly helps.

Hang 'Em High [one box/day]
Once per day, you can get a box of Questionite by being the highest rated fighter in the event. Since few people go through the Desert anymore, you can solo it and get it for yourself fairly easily.

Therakiel's Temple [3-5 questionte boxes/run]
Therakiel's Temple, the capstone of the Vibora Bay zone quests, offers battles versus several Vibora supervillains. It also has better writing, music, and set design than most of the game, so it's worth going through the battles and traps for that reason alone.

Questionite box [random]
About 1 in 512 critter defeats, you'll get a box of Questionite. The value is random and can be as high as 1500 Questionite for one box, but averages 200 Questionite.

Every day, you can refine 8,000 questionite ore into spendable questionite. Here's where you can use it.

Questionite Store
In the lower-right corner of the minimap, there's a button marked "Store." This store exclusively deals in Questionite.

The most important items to purchase here are in the Set Devices section: the Armadillo gear set, when you have 3 pieces together, will also grant a +25% Physical Damage Resistance bonus. This bonus is a huge boost to your survivability, because over three-quarters of the damage dealt in this game is physical (Crushing, Slashing, or Piercing) thanks to powers from the Might and Mutinitions powersets being omnipresent. It's only 33,000 Quesionite to grind the Boots, Ring, and Glasses, so every character in your account should do so right away.

One other important device to grind are the Necrullitic Elixir (best self-healing power in the game, 400,000 questionite)

Legacy Aura Vendor
The Legacy Aura vendor sells auras for 80,000 questionite each.

Unmodding Gear
After a certain level, removing a mod from a piece of gear you own will cost Questionite.

Questionite Exchange
By far the most important use of Questionite, you can buy Zen off of premium players here. The exchange rate fluctuates but averages 500 Questionite = 1 Zen.

The most important item you can buy on the Zen Store are Cosmic Keys of Power for 100 Zen. Each Key allows you to open one Lockbox, which gets you 1-2 pieces of Drifter salvage. Drifter salvage is used to purchase the most important items in the game: Justice Gear primaries (10 drifter salvage each) and the Legacy Devices (50 to 250 drifter salvage). Important Legacy Devices to grind are Teleiosaurus Pheremones (250 drifter salvage), Ice Grenades (250 drifter salvage), and the Nightmare Generator (50 drifter salvage).

You can also use the Cosmic Keys of Power to open lockboxes in order to unlock lockbox series items. A few lockboxes even have worthwhile items in and of themselves.

Yes, you'll have to spend 8 days - assuming the market is on your side - for each key. If you have the patience of Job, grind Questionite to earn the Aurum Pack, which gives you 20 keys for the price of 18 as well as two Aurum Pack-exclusive pieces of heirloom equipment.

The Zen store is also the only way to get more character slots, bonus bag slots, high-capacity bags, bonus costume slots, certain travel powers, and the exploit-friendly hideouts. So no matter your goal, grinding Questionite is a must-do.