Some of the Combos
Caltrops + Sydri, Galvanic Genius = Any attackers without indestructible immediately die. Sydri turns Caltrops into a 3/3 with lifelink and deathtouch. Both keywords trigger when damage is dealt and you know the rest.
Sydri, Galvanic Genius + Voltaic Construct + Thran Dynamo = Infinite colorless mana. Animate Dynamo, tap it for 3 colorless, use 2 of it to untap with Construct's ability, wash rinse repeat for infinite colorless. Replace Dynamo with Gilded Lotus to produce infinite colored mana.
Sydri, Galvanic Genius + Mycosynth Lattice + Dross Scorpion = Infinite Land Destruction. While Dross Scorpion and Mycosynth Lattice are out, tap a land that produces blue, animate an opponent's land into a 0/0 that immediately dies, Dross Scorpion will see an artifact go to the graveyard, therefore untapping the blue land you spent to animate the land. Wash, rinse, and repeat until all lands aside from yours are destroyed.
Thopter Foundry + Sword of the Meek + Krark-Clan Ironworks = Infinite Life and Colorless Mana. Step 1) Sac Sword to the Foundry, producing 1 life and a thopter token. Step 2) Sword comes back equipped to the thopter. Step 3) Feed the thopter to ironworks producing 2 mana. Step 4) Use one of the colorless to feed the sword to the foundry, repeating the cycle.
Sharuum the Hegemon + Phyrexian Metamorph/Sculpting Steel + Disciple of the Vault = Infinite Life loss. Start by having Sharuum and Disciple on the field, then play Sculpting Steel or Phyrexian Metamorph copying Sharuum, put the legend rule on the stack, sacrifice original Sharuum, use the copy's ability to recur the original, sacrifice the copy, repeat till you win.
Rings of Brighthearth + Basalt Monolith = Infinite colorless mana. As Snickles@EDH_only graciously pointed out, my understanding of the interactions that go into this combo was flawed, so in their words, this is how the combo goes off:
1) tap Basalt Monolith for 3
2) use the 3 to activate the untap abiltiy of said monolith
3) respond to the activation of the untap by paying 2 for Rings of Brighthearth to activate the untapping a 2nd time.
4) let the rings' untap trigger resolve
5) respond to the original untap activation (which would do nothing, as untaping an untapped permanent has no effect), you tap the monolith for 3, then let the original resolve.
6) go to step 1
Nets 1 colorless mana per cycle (provided you have the 2 cards, and 2 mana to spare before you start.)
Infinite Colored Mana combo + Staff of Domination = Infinite Life and Cards. Combo is pretty straightforward.
Walking Ballista + Infinite Mana Combo = Infinite Damage. Use an infinite mana combo to cast Walking Ballista for 1000 (just an example), then unload until all opponents or creatures are dead. Add Sydri, Galvanic Genius for some extra kick.
Sydri, Galvanic Genius + Aetherflux Reservoir = Dome All Opponents To Death. Once you have 50+ life, use both of Sydri, Galvanic Genius's abilities to give Aetherflux Reservoir lifelink and deathtouch, then proceed to kill everyone.