I personally adore janky combos. They're basically half the fun. So... what are your favorites?
A couple that I've thrown together recently:
Generous Patron + Proliferate: This basically reads "draw X cards whenever you do [blah], where X is the number of creatures your opponents control with counters on them". I like doing it with +1/+1 counters, because I'm "nice".
Fertilid + Amulet of Vigor + Evolution Sage: This gives you ": Search your library for a basic land card, put it onto the battlefield, then shuffle your library. Proliferate." If your mana base is primarily basic lands, this can almost double your lands every turn (If you start with X lands, you end up with 2X-1).
Simic Guildmage + Hapatra, Vizier of Poisons: Generate a snek for . More usefully, you can then spend to remove a -1/-1 counter from your guys and get a CIP/death trigger (dump the counter on a snake token, get a new snake token).
Throes of Chaos + Harness the Storm:You get anywhere from two spells to six spells for every land card you discard, depending on what else is in your graveyard. I think I'll be building this deck when Modern Horizons comes out... Each land turns into 1-4 random spells with CMC 3 or lower, depending on how many Throes are in your graveyard. I was misremembering Harness the Storm there. The only reason this is more impressive than it'd normally be with retrace is because you get double storm count.
This isn't exactly a combo but in my Jodah EDH deck, I once cast a Howl of the Horde (with raid) with mana from a Primal Wellspring and I cast Worst Fears (everything for free due to Omniscience), so I effectiely stole my friend's next seven turns. The best part is that the deck is entirely built from draft chaff and random boosters I bought.
"Reading the card explains the card." -Tolarian Community College
Now, normally, I hate TakingTurns.archetype, but this, I love. Why the seeming dichotomy, if not outright hypocrisy? It's because Taking Turns usually starts going off around turn 4 or 5, whereas Dinos with Helmets can only ever go off like that post turn 8 or so, more than enough time to guarantee interaction, one way or another.
Lady Mapi : Is the Bag of Holding necessary here ? (Of course it's a must have in this deck but the combo could work without it no ?)
It's not necessary to the combo, but it really does smooth things out.
A fun pauper combo: Firebrand Archer + Curiosity or Sigil of Sleep. Turn all of your spells into either massive card-draw (one card for each opponent), or mass-bounce things. Honestly, there isn't anything special about the archer - this works with any of the "hurt everyone when I do things" cards that red gets. If you're going the Curiosity route, you can replace the enchantment with a Tandem Lookout if you want something less risky than an Aura (the Aura does trigger your Archer, though).
You want the real magic? Firebrand Archer + Scuttlemutt + Ghastlord's Helm. You can replace the Scuttlemutt with basically anything that can change a creature's color to Black. But yeah - instant-speed mass discard. You will get punched for this, I think.
Tap Itlimoc for mana, tap the Hierophant to untap it, then play a creature. Chulane drops a land, then the Hierophant untaps. As long as you have lands in your hand, this little engine will generate both card draw and craploads of mana.
1) First Ibex triggers. You have two tapped 6/6's, two tapped 8/8's, and a tapped 10/10. 2) Beastmaster triggers. You have a tapped 6/6, a tapped 12/12, two tapped 14/14's, and a tapped 16/16. 3) Copperhorn triggers. You have an untapped 6/6, a tapped 12/12, two untapped 14/14's, and an untapped 16/16. 4) Tap the Goats to make the Bridge Troll happy. You have an untapped 6/6, a tapped 12/12, two tapped 14/14's, and an untapped 56/56. 5) Second Ibex triggers. You have an untapped 62/62, a tapped 68/68, two tapped 70/70's, and an untapped 112/112.
The best part? It scales crazily with each creature you add. Getting all of these creatures onto the field is an exercise for the reader.
A surprisingly funny "defensive" combo in monored is Reckless Fireweaver + Curse of Opulence. Cast the curse on yourself, and you'll deal 1 damage to all opponents whenever they swing at you, and you'll get a Gold token. As a side note, Reckless Fireweaver is the worst cook ever - they can't even make a simple salad without burning the house down.