I'll just write whats on my mind and my experience in Gold (EUW):
In order to "beat" Nasus you have to understand what his goal is.
Wether his stacks, the huge damage boost he gains from his Ult or Spirit Fire's armor Shred Nasus has to fight you in close combat.
Outside of the weird Flash Q he can pull of once every few minutes he is quite literally a sitting duck.
What makes him strong is his amazing split-pushing, his better than average dueling power and debuffing your Marksman with wither.
If you want to defeat him either bully him in lane or exploit his weakness aka his mobility.

These guys and girls can easily outpoke and outdamage
early. What makes some of them problematic is their own weakness to ganks (Wither again) and that their trades will most likely push the lane towards Nasus tower. If Nasus is smart he won't feed or lose the lane but you can make his stacking so much weaker.

These three Champions are an interesting case as they look weak on paper but can easily outdmg and probably kill Nasus in a duel. Yi deals mixed dmg and ignores the movement slowing effects of wither. Nasus has no hard CC and therefore cannot interrupt Yi's meditate, allowing Yi to tank Spirit Fire and the odd Syphon. Vayne can tumble away and knock Nasus away, greatly reducing the effect of his wither. Her Silver Bolts hurt Nasus a lot and she can easily deal with wither if she has
or
.
Olaf is pretty much Nasus' worst nightmare in a fight. Nasus dmg is quite low and only spikes with his Syphon which Olaf can easily heal through with lifesteal and his passive. Ragnarök allows Olaf to completely ignore the effects of wither and thanks to his true-dmg spikes Olaf will easily outdmg Nasus in a duel and most likely kill him too.

Since Nasus can only run towards you in any fight, redirecting or preventing his advance with artificial terrain annoys him quite a lot. Anivia and Azir can scatter the enemy team, allowing you to kill more valuable targets as well as trapping Nasus outside of a Teamfight or buying your team time to focusfire him down (Even in his demigod form, Nasus **will **die once focussed.). Trundle is another special mention as he can defeat Nasus in lane too, offers great utility with his Pillar and can soften Nasus up via his Ultimate.
As for Jarvan, he is maybe the weakest of the bunch as he fights Nasus toe on toe but Cataclysm can also be used for the terrain instead for its damage. "Jarvan is helping!"

While these supports cannot beat Nasus in a duel they can however make him useless in skirmishes. Morgana's Spellshield provides her Marksman with immunity to wither and she can stop Nasus with Dark Binding. Thresh fucks Nasus over with his entire kit, either by pulling him back with Q or E, allowing Nasus target to escape with W or simply stopping him in his tracks with the Box. Janna, Nami and Alistar are similar in their functionality against Nasus. Tornado, Bubble and Pulverize keep Nasus in place (and make Yasuo's happy). Headbutt, Tsunami and Jannas' Ult can keep him away or reset Teamfights.
Janna is another special case in the way that she has a strong slow and her Q and R. Her passive and her Shield greatly increase her Marksman's chances of survival. If you are still concerned about wither: 

Another interesting combination. Cho'Gath can become just as tanky while dealing much more dmg. He has build-in sustain and stronger CC than Nasus and Feast can be used to chomp Nasus away (Unless are more valuable target is nearby mind you). Malzahar can easily freeze or hold lane against Nasus and on top of that, can be build in many different ways. You can exploit Nasus tankyness with
and Null Zone (W) while also using
's reduced effect with his E. Lastly, Malzahar's Ultimate allows him to lock Nasus down (applying both
and
. Preferably, inside a Null Zone.
Vladimir is another odd pick. As both are "weaker" early on Vladimir does outpoke and outsustain Nasus. Uninterupted, Vladimir might not win in the way that Nasus loses but both of them can hardly kill the other (Nasus can just walk away and Vladimir can pool away should he be to low, both will sustain themselves afterwards) and Nasus cannot push as long as Vladimir farms with E. Both of them can and will just farm away but Vladimir is much more dangerous in Teamfights thanks to the high dmg on E and his Ult's increased dmg effect. But wait there is more! Vladimir can make full use of
's slow with Transfusion, greatly reducing Nasus' mobility in skirmishes.
Ryze suffers from the same problem Nasus and Vladimir have in that his early game is pretty weak. However, Ryze can outdmg Nasus in Teamfights, can easily depush a lane and can Rune Prison him for ages.

Gragas is just a bully and in most cases just to tanky for Nasus taste but has to much CC (Slow, Stun, displacement) and hits hard with his W. Lee Sin has a strong early game and amazing ganking potential which is everything Nasus hates. Dragonkick is a great way to get Nasus away from your carry too.
Nunu just does not care about the enemy jungler AND Nasus. Not only can he cripple Nasus' jungler, providing your toplaner with more breathing room against him but Blood Boil and Snowball make it so much harder for Nasus to reach your squshies. Furthermore, as Nasus has only access to a slow, there is one player less on the field to interupt Absolute Zero/waste CC on Nunu.
I played Nasus a lot in Season 1, 3 and 4. While many things changed over the years Nasus has not changed that much. Note that most of the champions mentioned in my Wall of text do not "autowin" against Nasus like, for example, Diana vs Katarina (Unless huge differences in skilllevel are in effect) but can screw him over easily or make his game that much harder.
League of Legends is fundamentally a team oriented game and should be played as such. You don't have to defeat Nasus 1 one 1, but go ahead if you feel ballsy or are ahead of him. Despite his status as "the Raid-Boss", Nasus has the same weakness as them: Coordination and Teamwork.