Muktol

I would remove the following cards:
"Chandra's Phoenix" with 3 mana you can do more damage than this
"Keldon Marauders" 2 mana 2 damage and the option to attack once doesn't sound that good to me
"Lightning Axe". Damage is creature only, and you normaly don't want to shoot on creatures
"Banefire": Cards with 'pay X' are very mana intensive to play
"Flame Slash": Damage is creature only
"Goblin Grenade": If you have enought creatures to sacrifice for this, its OK, but otherwhise it's a dead card

With those many low cost spells, you can try to reduce the number of lands to 20 or maybe even 18.

Suggestions as replacement:
Creatures: "Ball Lightning", "Hellspark Elemental", "Vexing Devil", "Vexing Shusher" (Sideboard against control) or "Young Pyromancer" (For longer games)

Spells:
"Seal of Fire", "Shard VolleySorcery" (not more than 3 times, it's a finisher), "Forked Bolt4" (if you have to deal with some small creatures), "Rift Bolt" or "Wheel of Fate" (Carddraw)

Greetings
Muktol

I would try focusing either on the aggro or the burn plan, mixing both normaly wont be that good.

Some ideas:
Reduce "Arms Dealer" to 3, you don't want two of them on the board or in your hand.
Remove "Goblin King" for some more "Goblin Chieftain", ideal would be 4 chieftains
"Krenko, Mob Boss" could be used one more time, but this is a "could", not a "have to"
Remove "Raging Goblin", there are much better goblins than this one

Some suggestions:
Equipment: Infiltration Lens (Carddraw is never wrong)
Creatures:Bloodmark Mentor (First strike for all your red creatures); Goblin Wardriver (Battlecry); Mogg Sentry (cheap goblin and good defender in your enemys turn); Mogg War Marshal (Replaces himself with a token); Spikeshot Elder (converts spare mana into damage, even more usefull when pumped up); Warren Instigator (THE goblin you want on the table to speed up your game)
Enchantment: Quest for the Goblin Lord (cheap and good pump for all your goblins)
Sorcery: Goblin Grenade (converts goblins into damage, can also be shot on players (not like Arms Dealer) to make the final move)

Greetings
Muktol

I think we all know such moments ;)

I would change some of the numbers here ;)
"Goblin Chieftain" up to 4 and remove "Goblin King" instead. Your goblins need haste, especially "Krenko, Mob Boss" and the load of tokens he produces
"Goblin Wardriver" up to 3, and "Krenko, Mob Boss" down to 3, since he is legendary, you don't want to have him twice in your hand.
"Burn at the Stake" down to 2 or 3, again this is a finisher and you don't need it from the beginning. In my goblin deck (OK, I play with 18 lands) I normaly never see that much mana on my side of the table ;)
"Teetering Peaks" down to 2 or 3, great for late-actions when you allready have enough mana, but in erly game, it slows you down.

Suggestions:
Quest for the Goblin Lord (Enchant), Bloodmark Mentor (Creature), Furystoke Giant (Creature, Finisher), Mogg War Marshal (Creature, works great with Quest for the Goblin Lord), Spikeshot Elder (Creature), Mogg Sentry (Creature)

Greetings
Muktol

Remove "Lightning Axe", it's creatures only, and "Staggershock", 4dmg for 3 mana is not that good.
Reduce the number of "Banefire", it's a finisher, so you dont need in in your starting hand.
I would also change from "Pyromancer Ascension" to "Quest for Pure Flame"
Put "Skullcrack" into your sideboard, not every deck so much lifegain that you need to worry about it.

Some suggestions:
Creatures:
Ball Lightning, Hellspark Elemental, Vexing Devil; They are all more like burn spells rather than reall creatures

Other Spells:
Seal of Fire (cc1 2dmg), Magma Jet (cc2 !SCRY 2! 2dmg), Shard Volley (cc1 3 dmg), Forked Bolt (cc1 2dmg, you can remove utillity creatures with this one and still shoot 1 dmg on your enemy)

Greetings
Muktol

Suggestions
Equipment: "Loxodon Warhammer", "Basilisk Collar"
Artifact: "Well of Lost Dreams", usefull in longer games (And I think lifegain matches normaly last longer ;) )
Creatures: "Serra Ascendant", best beater lifegain can get; "Martyr of Sands", your enemy will know what you have, but for 3 x cards life, this should be irrelevant; "Ranger of Eos", can tutor you cc1 creatures
Enchantment: "Cradle of Vitality"
Sorcerys: "Proclamation of Rebirth", "Survival Cache"
Land: "Miren, the Moaning Well"

I have tested "Markov Blademaster" in my own vampire deck, and found it to 'weak'. Even with "Blade of the Bloodchief" it needes to much support to do it's job properly. If you manage to get it through you enemys defences it's great, but otherwise it will only end like an insect on a cards windshield *splatter*. You could change to something like e.g. "Vampire Lacerator" or, if you want to work with many +1/+1 counters, "Falkenrath Exterminator"
You should also try to focus un either "Curse of Stalked Prey" or "Rakish Heir". I prefer the curse, because it's more difficult to remove for your enemy.
Fot "Vampire Nocturnus" I have no expirience in a B/R deck. To work well, you should have somithing like the 'Scry X' abbility. If you relly on luck, it can happen that your vampires stay grounded for some turns. (Personally I also dislike the 'Play with the top card of you library revealed' because your enemy can see, and easily react, what you gonna do)
You also could remove the number of lands to 20. With the free spaces, I would add some more point removals like e.g. "Go for the Throat", "Lightning Bolt" or "Terminate".
A faster alternative to "Rakdos Guildgate" would be "Blackcleave Cliffs"

Greetings
Muktol

I would remove "Fencing Ace" for e.g. "Elite Inquisitor"
With so many low cost spells you can try to reduce your lands to 20, or maybe even 16
"Mentor of the Meek" would be a good choice for carddraw and "Thalia, Guardian of Thraben" against anything that runs many non-creature spells but I don't see anything I would remove at the moment. If you feel that you don't like a card, give one of those a try. ;) . Same thing with "Champion of Lambholt" it is a great card, , like papercliptrip said, but I wouln't know what to change at the moment.
"Bonds of Faith" is a great control/ buff card and "Call to Serve" made my day often enough
I run "Sublime Archangel" as finisher in my own (modern) Human Deck.

If you want to make a RDW deck, I can't help you, I have never played one of those, but If you wan't to make a pure burn deck, here are some ideas:
Remove "Charmbreaker Devils" and "Fire Servant" and replace them by "Hellspark Elemental" and/or "Vexing Devil". You can put those into your sideboard, and if you feel that the match takes longer than expected (e.g. against lifegain), you can board them in after the first round.
Like ergon314 allready said, remove "Curse of Bloodletting" for "Quest for the Pure Flame". The curse is more for midgames, wich you normaly don't want to get in.

I would furthermore remove the following cards:
"Brimstone Volley": Normaly you don't want to shot on creatures, so the morbid wont trigger.
"Incinerate": Your main target is the enemy player, and creatures that can be regenerated are normaly expensive and slow.
"Reverberate": Most of your damage spells should be cc1 and do 2-3 damage, and a cc2 copy of a cc1 spell is not really effective. If you're using cc3+ spells, you can think of it, but normaly a burn deck focuses on cheap and fast spells.
"Seething Song": I think this comes to late to be of great use. Within T3, if everything goes well, you have 3 cards in your hand and 3 lands on the board. One of those handcards is Seething Song and the other two are cc1 oder cc2 spells, so you can't really use the whole mana you're getting from the spell.

"Reforge the Soul": If you want carddraw I would change to "Wheel of Fate" as it is more stable in it's costs.
If you want to stay modern legal you also should remove "Browbeat"

Here are some ideas to replace the spells you remove:
Seal of Fire (cc1, 2dmg, player or creature), Pyrite Spellbomb (cc2, 2dmg, player or creature, possible carddraw), Magma Jet (cc2, 2 damage, player or creature, scry2), Shard Volley(cc1 3 dmg, player or creature), Forked Bolt(cc1 2dmg, plaayer and/or creature), Lava Spike(cc1, 3dmg, player), Rift Bolt (cc1, 3dmg, player or creature)

Greetings
Muktol

I use "Thraben Doomsayer" and "Mentor of the Meek" as card producing machine in my own human deck. Works very well in longer games, and safed my day once or twice for sure ;)

"Mentor of the Meek" is not a really good choice here. If you have 1 "Honor of the Pure" on the field only "Boros Elite" and "Champion of the Parish" will trigger the effect, with 2, nothing will.
I would also just use 2 "Path to Exile" and 2 "Oblivion Ring". The free slots could be filled with "Bonds of Faith" or "Call to Serve" (Flying doublestrikers are really bad news for your enemy ;) )

The question is, what do you want to cast when "Cast Through Time" is on the table?

I play "Chronozoa" as a second win- option in a similar Deck. It also serves as counter-safe, and those can easily be moved with "Power Conduit".
http://www.mtgvault.com/muktol/decks/counter-transfer/

Creatures:
I would change from "Crosstown Courier" to "Shriekgeist". The spirit hast evasion and it is far more likely that he can really deal damage to your enemy and thus mill him. If the attacking creatures have some sort of evasion, you could also remove "Tricks of the Trade"
Think of removing all "Consuming Aberration" for one more "Mirko Vosk, Mind Drinker". With the free spaces you could up "Jace's Phantasm" to 4 and "Duskmantle Guildmage" to 3, or add 3 "Wight of Precinct Six".
Planeswalkers:
Decide either for Jace or Lilian and remove the other one, in a mill deck I would prefer Jace
Sorcerys/ Instants:
I would remove "Grisly Spectacle", you normally don't want to keep 4 Mana unused in your pool. Use the free place to up the number of "Dimir Charm" to 4 .
"Mind Grind" will be of to little use with only 20 Lands, and you got yourself better alternatives. Use the free slots to up "Mind Sculpt" and "Pilfered Plans" to 4, or think of adding "Dream Twist" instead.
I have no experience with "Reap Intellect" but it seems awfully expensive. Effective for sure, but expensive. 5 mana for 4 cards, 6 mana for 8 is expensive. You could remove annoying cards from your enemy's hand, but this spell comes T5+ without ramp and normally your enemy wont have that many cards on his hand left, the dangerous pieces will be allready on the board.
Lands:
I would remove 3 standard lands for "Nephalia Drownyard". It is a You can mill your enemy, even you are in topdeck modus and the chance of drawing the right card is small.

I Changed some things recently:
Mainboard
-1 "Bloodmark Mentor" (I don't want to have 2 of them in my hand)
+1 "Furystoke Giant" (Finisher, combined with "Goblin Chieftain" and "Krenko, Mob Boss" he can be really ugly ;) )

Sideboard:
+2 Zo-Zu the Punisher (Thanks to patzebat and his goblindeck)
+4 Vexing Shusher

"Quest for the Goblin Lord" is a nice piece of enchantment for goblins. It also works very well with "Mogg War Marshal"
You could also think of "Goblin Lackey" (Not modern legal) or "Warren Instigator". Combined with "Infiltration Lens" they can make your enemy sweat: Block and let you draw card (and normaly loose a creature due to doublestrike) or don't block and risk 2 goblins for free on the field.
You could also try to reduce the number of mountains to 18-20. The mana curve of this deck is pretty low, so it should work.
As finisher I personally use "Furystoke Giant" on my goblin Deck

Why not keep in mono-red?
e.g. http://www.mtgvault.com/muktol/decks/r-burn/

It's worth a try. I'm using 16 Lands in my burndeck ;)
http://www.mtgvault.com/muktol/decks/r-burn/

With so many cc1 spells you can think of reducing the number of mountains to 18. But you'll have to test this carefully.