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Recently, I noticed something that is vaguely mentioned in many codexes and even the rulebook. Faction less units.
While I know that fortifications are factionless, this is still strange, because this is noted in some codex es that have no fortification slot.
Now, to the mercenaries.
I was thinking of taking some catachan and making them into mercenary models, which would be factionless.
Anyone have any ideas for these guys' rules?
Ideally you should be able to field them individually, they could be stubborn, they should have a large range of weapons to choose from , and they should be characters for challenges.

Right, I'll give this a crack.

Mercenaries

Scout-75 Points
Infantry (Character)

WS-4
BS-4
S-3
T-3
W-2
I-5
A-3
Ld-9
Sv-4+

Wargear
Space Marine Shotgun
Bolt Pistol
Baseball Bat (AP4 CCW)
Bonk! Atomic Cola-Once per game, at the start of a game turn, the bearer of Bonk! Atomic Cola can drink it. Until the beginning of the next game turn, the imbiber has a 3+ Invulnerable save and adds +1 to any cover saves he makes.

Special Rules
Independent Character
Hit And Run
Fleet
Move Through Cover
Stealth
Infiltrate
Dunestrider

Soldier-50 Points
Infantry (Character)

WS-3
BS-4
S-4
T-4
W-3
I-3
A-3
Ld-9
Sv-3+

Wargear
Missile Launcher (With Frag, Krak, and Flakk Missiles)
Space Marine Shotgun
Trench Shovel-S User AP5 CCW

Special Rules
Independent Character
It Will Not Die
Relentless
Rocket Jump-During the shooting phase, the Soldier may choose to fire a rocket at his own feet in order to move further. Fire either a Frag, Krak, or Flakk missile at himself-he automatically suffers a hit with the Strength and AP of the missile (centering the blast of the Frag missile over the Soldier in the case of Frag missiles) with no cover saves allowed. He may, assuming he survives the hit, then immediately move 2d6" (Frag), 3d6" (Flakk), or 5d6" (Krak) ignoring all vertical distance.

Pyro-60 Points
Infantry (Character)

WS-4
BS-3
S-4
T-4
W-3
I-3
A-3
Ld-9
Sv-3+

Wargear
Twin-Linked Heavy Flamer
Flare Gun-Range 12" S3 AP4 Pistol with Ignores Cover, Blast, and Deflagrate
Power Axe
Asbestos-Lined Suit-Provides a 3+ FNP against flamer weapons

Special Rules
Independent Character
Fleet

Demoman-50 Points
Infantry (Character)

WS-5
BS-4
S-4
T-4
W-3
I-4
A-3
Ld-9
Sv-3+

Wargear
Astartes Grenade Launcher
Sticky Bomb Launcher-Range 18" S4 AP5 Assault 3 Blast weapon. When the blast marker is placed, the Demoman can choose to either detonate the blast immediately (resolving the shots as normal) or leave them there, in which case, anyone directly under the center of a blast marker suffers a S3 AP- hit as the explosive bounces against them. Leave the blast markers in play. At the beginning of any shooting phase (including his opponent's) the Demoman may detonate all Sticky Bomb blast markers he has laid down, causing anyone underneath the blast marker to suffer a S4 AP5 Barrage hit for each blast marker they are under.
Bottle (CCW)

Special Rules
Independent Character

Heavy Weapons Guy-80 Points
Infantry (Character)

WS-3
BS-4
S-5
T-5
W-4
I-2
A-3
Ld-9
Sv-3+

Wargear
Minigun-Range 24" S5 AP- Heavy 10 ranged weapon
Space Marine Shotgun
Fists Of Fury! (CCW)

Special Rules
Independent Character
Slow And Purposeful
Feel No Pain

Engineer-75 Points
Infantry (Character)

WS-3
BS-3
S-3
T-3
W-3
I-3
A-3
Ld-9
Sv-4+

Wargear
Space Marine Shotgun
Bolt Pistol
Wrench (CCW)
Destruction PDA-S-1 AP- Melee Specialist Weapon Armourbane
Construction PDA-Allows the bearer to, if in base-to-base contact with a Vehicle, repair it for one hull point on a roll of a 2+ instead of shooting in the shooting phase. Also allows for the construction of engineering pieces. Engineering pieces come in two varieties-Sentry Guns and Dispensers. To construct an engineering piece, the Engineer must spend a shooting phase building the piece. He can then spend subsequent shooting phases (up to 2) improving it.
The Dispenser provides the IWND rule to all friendly models within 3". At level 2, it provides the FNP 6+ rule as well. At level 3, it allows all guns to fire one extra shot each time they are fired for friendly models within 3" (for example, a boltgun within 12" would fire 3 shots, or a Grav-Cannon would fire 6).
The Sentry Gun is a T5 2W immobile artillery model that has a range 30" S4 AP5 Heavy 3 gun that automatically fires (starting the turn AFTER it was constructed) at the nearest enemy at BS 2. (The Engineer can manually override the Sentry Gun, allowing it to shoot at his BS and at any target within range.) At level 2, it is a T6 2W model that has a 36" S5 AP4 Heavy 6 gun that fires in the same fashion. At level 3, it is a T7 3W model that has a 36" S5 AP4 Heavy 6 gun and a Cyclone Missile Launcher with Frag, Krak, and Flakk Missiles.

Special Rules
Independent Character

Medic-60 Points
Infantry (Character)

WS-4
BS-3
S-3
T-4
W-3
I-3
A-3
Ld-9
Sv-4+

Wargear
Syringe Gun-Range 18" S1 AP4 Assault 3 Poisoned 4+ gun.
MediGun-Range 12" gun? When firing the MediGun, select one friendly within range. The model gains the FNP 4+ and IWND rule (if it already has either, increase the roll by 2). If the MediGun is "fired" at the same model two turns in a row and the model is at max wounds, it may gain a single extra wound (up to half again its max starting wounds, rounding up). These wounds go away immediately if the Medic dies or if the MediGun targets another model. A model within range of the MediGun may start the game under its effects-you do not have to wait for your first shooting phase.
Hacksaw (AP 5 CCW)

Special Rules
Independent Character
Ubercharge-Once per game, so long as the MediGun has been fired for at least two turns in the game so far, the target of the MediGun and the Medic may gain a 3+ Invulnerable save at the beginning of the shooting phase, lasting until the controlling player's next shooting phase.

Sniper-80 Points
Infantry (Character)

WS-3
BS-5
S-3
T-4
W-3
I-3
A-3
Ld-9
Sv-4+

Wargear
Stalker Sniper Rifle-48" SX AP4 Heavy 1 Sniper
Macrostubber
Kukri (AP 5 CCW)

Special Rules
Independent Character
Deadeye-The Sniper can spend turns aiming instead of firing. If he does so for one turn, his next shot gains a +1 bonus to the wound roll. If he does so for two turns, he gains a +2 bonus to his wound roll and the shot gains the Ignores Cover special rule. If he does so for three turns, he gains a +2 bonus to his wound roll, Ignores Cover, and Twin-Linked. If he does so for four turns, he gains a +2 bonus to his wound roll, Ignores Cover, Twin-Linked, AP3, and Instant Death. If he does so for five turns, he gains a +2 bonus to his wound roll, Ignores Cover, Twin-Linked, AP2, Shred, and Instant Death. These turns must be consecutive, and only apply to his next shot.

Spy-75 Points
Infantry (Character)

WS-5
BS-4
S-4
T-3
W-2
I-5
A-3
Ld-9
Sv-4+

Wargear
Bolt Pistol
Butterfly Knife (AP 6 CCW)
Disguise Kit-This grants the Spy the Infiltrate Special Rule, and he may infiltrate within an inch of any enemy models.
Cloaking Device-This device can not be active for two turns in a row. While active, only Snap Shots may be fired at the Spy.

Special Rules
Independent Character
Infiltrate (See above)
Backstab-The Spy is able to attack characters currently in a challenge that he is not a part of. If he does so, his attacks gain the Rending and Shred special rules.

I'm going to skip the TF2 post and try and answer this one seriously.

It sounds like you're looking for something along the lines of Blackshields (Space Marines that have gone off-mission and rejected the Emperor and Horus both), only in 40k and for normal humans. You'd probably run into some conceptual overlap with Penal Legion or Rogue Trader forces, most of these suggestions could probably be taken generally.

First off we're probably looking at a veteran statline; mercenaries tend to have more combat experience by virtue of following wars around as they happen instead of being stationed in one spot or going around at the speed of the Administratum. They're not necessarily going to be scarier than hardened Guard veterans, but they aren't going to be recruiting a steady stream of conscripts either.

On the subject of army rules I'm not sure about army-wide Stubborn, the Corsair rule that gives them one Ld value for normal use and a lower one for Regroup tests could be an interesting alternative. You get higher Ld for more staying power than normal Guardsmen, but your troops aren't about to stick about and get themselves killed in hopeless situations. I'm also liking the Blackshields' limited-resources-derived mechanics (+1 to the roll to go first, and can't have more vehicles than non-vehicle units).

Equipment is definitely going to need to be widely varied, depending on what lore implementation you're going for (e.g. a heretically-minded Rogue Trader might have access to pulse weapons from his work with the Tau, a mercenary company frequently employed by the Mechanicum might have galvanic rifles, et cetera). Model-by-model small arms are definitely necessary, more organized mercenary outfits may try and keep their troops uniformly equipped but the option for a scrounged feel is definitely necessary. Running off the Blackshields as a starting point again I'd say start everyone off with a laspistol/autopistol and close combat weapon, and give options that add on top of that.

Given the hour and my sleepiness I will make mention of Pariah gear (stripped-down versions of basic Imperial equipment that exist to be more flexible and easier to supply and maintain, ex. the 16" range Assault 2 Pariah bolter that requires its wearer to make a Disordered Charge if they fire it) before turning in, will elaborate further in the morning.

Have a look at the Tyrants Legion army list from Forgeworld.
Renegade Marauders are literally mercenaries, and, as sugfested, have a wide range of gear options (from carapace armour to infiltrate to power swords to assault weapons to part-of-the-squad ogryn analogues).

They definitely aren't stubborn -quite the reverse. They have a special rule called "in it for the money" which means they are not allowed to rally once broken.

Ork Blood Axes will hire themselves out to the highest bidders.