I've been toying with this build lately, and it works as a solo mid, or on bot. However, since this build does mostly magic damage, it may throw off your team comp.

And you may ask, "Why AP varus when his AD scaling is very strong?" Well, I ran some numbers, and two of his skills scale incredibly well with AP. First off, his ult has a 1:1 ratio, and is a hard CC, simple. Next, the on-hit effect of his W doesn't do much to make up for it, but the proc does! An extra 1% of their max hp for each 50 ability power you have, and that stacks 3 times! This build will have around 600 AP fully built, including a DFG and lich.

The largest thing that makes this build work is Blighted Quiver. To do the largest burst, there needs to be 3 stacks. If the attack speed is too low, you won't get the nuke off before they're on your face. And what a nuke it is! It deals damage based on a percentage of their health, so even tanks will cry (Amumu will have to stop and just go into a coma). Quintessences are for move speed, since varus lacks a reliable escape skill.

Full AP and damage increse, bonus to Surge and Flash, move speed, and .... yes... creep damage. As an AP I had problem last hitting, and this helps. It also makes a slight difference once you have Madred's Bloodrazors younger brother, Madred's Razors, as you'll be able to push lane incredibly fast with Varus' passive, then gank!

The only non AP items are boots, and Bloodrazors. Unlike most AP varus builds I choose not to run Malady. Reason is Malady stacks 4 times, and you'll cast after 3, which doesn't maximize DPS or Malady. Also, it has a mere 25 AP. I filled Malady's slot with Lich Bane, for the movespeed and extra nuke.

Rylai's looks terrible with Varus' skills. But there is a reason for this madness. Deathfire's does the most damage the more HP the victim hax, thus you want to lead with it (unless they have Banshee's). Rylai's will apply the full slow with Deathfire's, keeping the vic nearby enough to be nuked.

I did this rushed on my lunch break, so I can add more later. In the meantime, I'd love to hear feedback.