Ill have to see how the damage shifts with Iceborn and possibly a BT. Youd lose the movement speed from TF, I dont know TF just gives her so much of everything.

My build on her was:
Zephyr
Rageblade (this works very well because of her E and rageblade's passives)
Ninja tabi
Runic bulwark
Black cleaver
GA or BT if I need tanky or damage. I almost would say gunblade because she is an AD caster with a nice AP ratio on E, but it wouldn't work out.

BC, Zephyr, TF, Runic, Tabi/Merc, then a filler item, definitely not Zeke's.

Building her mostly tanky is a really good way to go, because she can do all the damage with just a little bit of bonus AD, her scales are immense. There's almost no reason to go mostly damage on her because of this. I built her in a mostly tanky role last I played, and she dunk dunk dunked everyone because not only was I unkillable, I was doing all the damage with tank items.

Honestly, all of these'recomended builds' seem pretty meh to me, she needs different things at different parts of the game, i've seen so many bad VI's build like what you guys recommend and become **** lategame, or rush phage, and honestly it sucks.

I've played her for almost 2 solid days on pbe, i can say without a doubt
http://puu.sh/1yztN
Is one of the best builds for her

It gives her EVERYTHING she needs

Boots are up to personal choice, situation though.
Her never ending slow to stick to enemies and punch them
Attackspeed for more punching
Tanky to survive while punching
Pen to make her punches hurt even tanks.
She needs so much damage to stay good lategame, she also needs lots of tankyness, this build gives her EVERYTHING she needs.

I know iceborn gauntlet isn't the best thing for her at first, but think of it, armor, cdr mana, and everyone of her E's and Q's gain the proc, on top of a 100% aoe slow that you don't gamble on the proc, she's very easy to kite when her Q is down, this helps her stick with people a lot easier, it's worth the tiny bit of ap you pay for that's not really used.

BT instead of black cleaver, if you want i guess? she already gets over 300 damage with this build, she could use life steal i guess but that's completely up to you, the cdr from bc seems to be more valuable to me.
50 more attack damage and some life steal vs all that delicious pen and cr, hp. your call.
Her whole kit plays off of killing things with her abilities and a couple autos, she's much more reliant on her abilities than auto attacks so life steal midcombat feels useless
I feel the pen and cdr to work better for her, if you're careful in lane 2 dorans blades her shield and a couple potions are all you need to keep her healthy through laning phase.

I build Vi sorta like a bruiser with some sustain. Every build depends on the situation and your play style but mostly I go:

Phage - Vi lacks any type of CC - later upgraded to FroMal for the % Health bonus on her Passive and of course more SLOW
Vamp Sceptor - Vi lacks any type of sustain meaning you rely too heavily on Health Pots which suck late game - Upgraded to BT later
Glacial Shroud - Nice CDR, Some Mana, and Armor - Can be upgraded later to Frozen Heart
Hexdrinker - Need some MR? This is it while not missing out on too much AD - Can be upgraded later to Maw

This is a pretty balanced build giving her survivability and damage and seems to work well for me. As I said though every build is situational. Some might want to grab a GA or others might rush the BC for the armor reduction, health and dmg. It all depends on you. I feel since she lacks sustain and CC that this works well. If the other team doesn't have much AP but a lot of AD DPS then go Randuins grabbing a Wardens Mail early on. Every situation is different so just experiment and find what works for you.

I haven't tried many of the newer items but Iceborn doesn't seem like a good fit since most of her abilities scale on AD. I know they added a small AP scaling on her E but seems pointless to pursue that. Also, BC is a good early item but I see no reason to rush it. I've also heard the Ravenous Hydra works well with her and if you need to cleanse some pesky CC then choose the Mercurial Scimitar which is built from a QSS but also gives AD so all around great item.

I went
Trinity Force
Black Cleaver
Maw of Malmortius
Blood Thirster
Bulwark

Ok after trying her again with some of the recommendations on here this is what i've come to.

Blade of the Ruined King - Works well with her but still inferior to BT so just get a BT and don't bother with this item
Black Cleaver - Even after the nerf this item is still a GREAT buy. Gives her DMG, health, CDR and Armor reduction and not too expensive.
Ravenous Hydra - An INCREDIBLE item giving her massive AD boost and splash dmg. However, the smaller item which is the Tiamat gives her the splash and 25 less AD then the Hydra so if you just want the splash just get the Tiamat. It does not give you the life steal though which could be what you want if you didn't get a BT
Mercurail Scimitar - Works as advertised giving you some nice AD along with a cleanse if the team has a lot of CC. Although if you initiate with your Utli, you can make them waste all their CC trying to stop you!
Iceborn Gauntlet - This one is a mixed bag. The item is really expensive and not worth the coin in my opinion but the CDR, mana, Armor and bonus Physical Dmg is not wasted on Vi. The bonus AP on her E only amounts to like 30 extra dmg so not worth it for just the AP benefits. Honestly I think the Tiamat or the upgraded Hydra are much better items and if you just want the bonus Physical just get the Sheen and don't waste a lot on this item. Also the Frozen mallet gives a much better slow and a lot of health which helps her passive. Honestly, I don't know why you would want this item on Vi...

Thats my 2 cents on the subject but as I said earlier, every game is different and your build path SHOULD change depending on enemy team comp and what your team needs.

There seems to be a 50/50 opinion on TF. You people dont miss the movement speed?

Mallet -> BT -> Tiamat -> BC -> Hydra -> Defensive Item*

* -> Guardian Angel or Mercurial's Scimitar, what fits you best. If you do pick Mercurial's, a Ninja Tabi is welcome because ADCarries tear you apart.

She needs boots of swiftness. they are actually good boots now especially on Vi.