The Legend of Zelda:

So here the sword is a basic design. It is straight and has a gold hilt and a white blade.
The Adventure of Link:

As you can see, the sword is exactly the same: it has a gold hilt and a white blade. Perhaps this is the White Sword?
A Link to the Past:

Very similar design here, except that the hilt is brown and is slightly curved, but the blade remains the same. Since we all know what the Master Sword looks like and the fact that it hasn't changed, I didn't feel the need to post a picture of it.
Link's Awakening:
Like the LA shield, the LA sword is exactly the same as that from ALttP.
Ocarina of Time:

The Kokiri Sword is much more like a knife, but I'll describe it. The blade is white and the hilt is brown and curved and there is a red jewel set into it. Since we all know what the Master Sword looks like and the fact that it hasn't changed, I didn't feel the need to post a picture of it.
Majora's Mask:

The Kokiri Sword has changed a lot here. The hilt is now blue and yellow and there is no jewel set into it, plus the hilt is now straight.
Oracles:

Sword is very similar to the ALttP and LA swords, but is the same as the LoZ sword. It has a white blade and brown, straight hilt.
Four Sword Series:

The Four Sword remains exactly the same throughout FS, FSA and TMC. It has a curved, gold hilt and a white blade. Plus a jewel set into the hilt, that changes colour depending on which Link is wielding it.
The Wind Waker and The Minish Cap:


Here you can see that bothe the Hero's Sword in TWW and Smith's Sword in TMC are the same. The hilt is rounded and a sort of light brown grey colour, and the blade is white. Since we all know what the Master Sword looks like and the fact that it hasn't changed, I didn't feel the need to post a picture of it. The sword in PH is the same as the Hero's Sword from TWW.
Twilight Princess:

Bears a lot of resemblance to the LoZ sword, with the straight hilt and white blade, although the blade is considerably longer and the hilt is a mix of brown and grey.
So we know what the swords look like. Now let's group them:
1) LoZ and AoL: straight, gold hilt with white blade.
2) ALttP and LA: Curved brown hilt with white blade.
3) OoT and MM: Swords made by the Kokiri.
4) Oracles: Very similar to both ALttP / LA and LoZ / AoL swords.
5) FS, FSA and TMC: Four Sword remains the same throughout, with a gold curved hilt with jewel and white blade.
6) TWW and TMC: Round, grey hilt and white blade.
If you believe in this timeline:
OoT-MM-TP-TWW-PH-TMC-FS-FSA-ALttP-LA-OoS/OoA-LoZ-AoL
You'll notice that the swords seem to follow this.
OoT and MM has the Kokiri Swords, so they aren't really Hylians Swords, but MM has the Kokiri sword with a straight hilt.
TP has the sword with a straight hilt, so this may have been inspired by either the Kokiri Sword, or by looking at the length, the Biggoron's Sword, which also had a straight hilt.
TWW, PH and TMC have the same sword design, which is basically the same as TP's design except that the hilt is still straight but is rounded.
TMC, FS and FSA have the Four Sword which is the same in each game, with a curved gold hilt and jewel and a white blade.
ALttP and LA follow the design of the Four Sword except that the hilts are now brown but still curved.
The Oracles have the same design swords from ALttP and LA but now the hilt is straight.
LoZ and AoL retain the straight hilt but have now coloured it gold.
So there you have it. The sword's don't just drastically change from game to game, their design changes are small and seem to flow from game to game quite nicely. Hmm. Perhaps Ninty weren't lying when they said that they were trying to tie the games together? Well, tell me what you think of this.