Which profession can achieve permanent or near-permanent swiftness?

Elementalist

Elementalists have several ways to maintain 100% Swiftness uptime.

One is to put 20 trait points into Air Magic and select the Quick Glyphs and Inscription traits. This will make the Swiftness granted by your Glyph of Elemental Harmony last as long as the skill's recast time.

Staff Elementalists can combine Glyph of Elemental Harmony, Windborne Speed, and Static Field+Arcane Wave (Lightning/Blast combo). This works regardless of what traits you pick, but you do need to carry Arcane Wave for the blast finisher.

Dagger/Dagger Elementalists can combine Glyph of Elemental Harmony with the Zephyr's Boon trait in Air Magic and their Frost Aura and Shocking Aura skills, as well as Ride the Lightning and Updraft. As an added bonus, 5 points in Air Magic lets you move 10% faster when attuned to Air.

Engineer

The Speedy Kits trait grants Swiftness when changing kits.

All you have to do, besides having the trait, is keep on changing kits in order to keep your Swiftness up. You will need at least 1 kit skill in a utility slot in order to actually equip it. You can equip/unequip/equip the same kit to keep the swiftness flowing.

Guardian

Staff Guardians can use Symbol of Swiftness, which grants 8 seconds of Swiftness with a 15 second cooldown. For utilities, you can use Retreat (20 seconds swiftness) and Save Yourselves (10 seconds swiftness). Using a single cycle of those skills together will provide a total of 38 seconds of Swiftness.

I believe warriors can achieve permanent swiftness with the warhorn skill charge (10 s, 20 cooldown) and the elite Signet of Rage (30 s, 60 s cooldown).

To expand on Engineers (PvP specifically), I've been running a PvP build that focuses on maintaining swiftness and have enjoyed it:

http://gw2skills.net/editor/?fcAQJAqalspaen1y3F1LJxoCcG0j8WfAISR+x8nCsF;T8AAzyqEUJpSVliKqkMJJSymkLJZSjROjMHB

Key points:

• Infused Precision grants you swiftness after roughly every other critical hit.
• Sigils for chance on critical quickness.
• Runes for increased swiftness duration.
• Invigorating Speed grants you 5 seconds of vigor whenever you gain swiftness.
• The Slick Shoes secondary "F" skill gives you 5 seconds of ad-hoc swiftness to help fill the gaps.
• Secondary build focus: applying the burning condition.

In a PvP setting, I prefer to not be caught off guard while switching kits, but for perma swiftness agnostic of combat effectiveness it is a viable option.