Weird builds to try

Support Anivia, Top Lane Taric, Jungle Morgana & Jungle Zyra.

Tank AP Warwick, Jungle AD Nami

A weird but enjoyable buid is AD , His voidlings deal a % of his AD. So you spam spells and make an unstopable army of Hard hitting little bugs.

Plus they hit whetever ur ulting. So get as many voidlings out as possible, Immobilize them with ur ult and let the little buggers smash the shit outa the enemy.

AP/AS (not as good anymore without DFG tho) Seraph's+AP or Manamune+AD Magic pen build (those cleavers HURT) AP (excellent assassin actually, really good at countering AP heavy teams, should see more play than he does) AP (Probably the highest damage champion in the game, but not very bursty, and needs a LOT of protection) AD (Rush Trinity force into IE+PD+BT and you deal crazy burst with your AA-Q-AA combo) AD+Crit (W's steroid makes you surprisingly bursty with IE and some extra AD and Crit chance) AP Burn build (Rylai's+Liandry's=Spirit fire of DOOM! you can still farm stacks well with Lich bane or Trinity force, and build full tank after that) AP (you have insane burst, and if you build a lot of armor to go along with your AP, you deal great mixed damage)

AP Lucian mid and AD / AS Janna top are fun.

Tank AP AD Critical Strike

They still work, just weird lol

ap xin is easy. Nashor's, spirit visage, and deathcap. You can now face tank turrets and win.

AD annie can work but it just has no synergy. Everything good about annie comes from her burst which you really won't be using often. However ad support annie is a beast. AA-q poke constantly. This is honestly where ad annie belongs. I run my adc runes and utility masteries to get as much gold as possible then transition into ap. A long sword is very nice on her early too.

adc leblanc - I haven't run this personally but I have seen it a few times. Easily one of the safest possible adcs. Usually go for as much crit as possible and a bit of damage. ie, pd, shiv, yomuus in any combination that you would like. You can bypass the tank line completely and just kill the squish. It can wreck people pretty hard.

adc twisted fate - I absolutely love this. I don't think it's weird but I always seem to get bitched at when I play it. botrk, lw, pd, ie/shiv, bloodthirster. max E first then w. don't bother with q at all. I only put points into it when I have nothing else to level and then never use it. strong poke on every fourth attack with a passive AS buff. The all in potential at level two is pretty high and once you get rolling ult kills are easy. You're definitely going to want to get life steal and a fair bit of it. you're squishy as hell.

ap warwick - He can be an absolute monster if he gets snowballing.

Full ap amumu - It's just fun. Standard ap build with cdr. ult anything that so much as moves >.< And for more fun do the amumu insec. hook a tank then flash onto the carries for the ult. same thing as lee sin right?

on-hit AS Soraka jungle.

I love off-meta stuff. Jungle Braum is a ton of fun if you have him, AP Skarner mid does a crap ton of damage and has a massive shield. AP Irelia does a crap ton of burst damage.

AP darius.

I'm a fan of support splitpusher Shaco. Start with an Ancient Coin for sustain (with a little extra regen in your runes/masteries, you can place a box every time it's available) and scanner for removing enemy wards (or totem if you really want to be a master of vision control). If you keep boxes up in the river bush and tribush (if you're on blue side), you're practically ungankable. With a Caitlyn as your ADC, your lane is almost entirely ungankable (traps everywhere). Proceed to build Tiamat as soon as possible, followed by Statikk Shiv and Trinity Force. Your burst will be considerable, and your waveclear will be insane. You'll also be extremely fast (nigh-uncatchable because of Shaco's kit); I regularly skip building boots because Shaco can easily escape without much speed if you learn how to juke and blink over the right walls. I'd also suggest an Infinity Edge because it greatly increases your DPS and synergizes with both Statikk Shiv's proc and Shaco's Q minicrit.

Cooldown reduction is a decent stat to have as support AD Shaco (more W boxes, more Q invisibility, more E shiv throwing, and more clones), but you're perfectly fine with zero CDR.

In most matches, you'll end up catching your bottom lane opponents on a box sooner or later, then immediately ending the lane with a strong push (assisted by your ADC, boxes, and clone). I usually don't lose my tower because Shaco's boxes can greatly disrupt minion waves when they're hitting your tower. Either way, as soon as your lane is over, you use your Tiamat to push another lane and farm (while keeping yourself safe with boxes for vision). Once you have Sheen, Statikk Shiv, and Tiamat, your burst is considerable (though you probably won't 100-0 anyone until you get Infinity Edge); you'll become a great splitpusher, vision controller (without having to buy many wards!), and assassin, despite being a lowly support.

The main weakness of support Shaco is your lack of direct peel for your ADC. I usually take Ignite and Exhaust for extremely strong dueling/assassination power, plus Exhaust can make up for your lack of peel. You'll do much better with a coordinated/voice-chatting team because they're more likely to coordinate with your box placement. Your boxes can save your team's collective ass if they lose a teamfight, or allow your team to jump on squishier targets when they happen to step too close to a box.

Cinderhulk Jungle Zyra

It's pretty well known, but no one has posted it here that I've noticed.

AP

Snag a Lich Bane, get lots of AP and CDR, then blow people up or blast them from afar. It's really fun to E-W-Q into an unsuspecting enemy and instantly delete them. I have had some fun in match ups against LeBlanc too, but I suspect those would be harder to pull off the more skilled your opponent is.

Thank you so much for the detailed build

But the lane presence from smite or tp is gone then

Jungle Gnar w/ devourer, if this hasn't been mentioned yet. It was one of the nastiest games I have ever played. As well, AP tank Gnar. His stacks that burst into damage scale off AP. The first two hits will do almost nothing, but the third hit does a crap ton.