They were a type of light cavalryman in the service of Gustavus Adolphus during the Thirty Years' War. It is commonly accepted that the name comes from the Finnish battle cry of "Hakkaa päälle!", although there has been some dispute about the issue - especially as the troops tended to be known for their comparatively silent way of fighting. They didn't wear a 3/4 armor like their imperial cuirassier counterparts, and didn't tend to caracole, but the lack of armor was mainly a financial issue and their aggressive charging tactics didn't as such differ from Swedish light cavalry tactics of the period.
Warlord Games provides rules for Hakkapeliittas in their The Devil's Playground -supplement, but unfortunately they don't provide miniatures that are suitable as such. The pictures I've usually come across as depictions of the armor is a morion helmet and a simple breastplate (especially in the re-enactment photos, but the armours are not blackened and the breastplates tend to be very simple sheet metal affairs - I'm not sure about the historical accuracy here), whereas Warlord's miniatures have different variations of the lobster helmet due to it being partly molded to the plastics.
Then again, Richard Brzezinski states in Osprey's "The Army of Gustavus Adolphus (2)" -booklet that the Hakkapeliittas probably used Polish style helmets, ie the lobster-tail helmets if available, but usually wore little or no armor.
What all of this means, who cares?
Basically, I interpret this so that either the zischagge, a felt hat or a morion helmet are all acceptable options. I wanted my hakkapeliittas to stand out from the rest of my cavalry, so I decided to go with the morion helmet. I used the basic WG plastic infantry morions and modeled the hair for the cavalry using Magic Sculp.
I also thought that I wanted to follow Aulis J. Alanen's (a late finnish professor of history at the University of Tampere) description of the hakkapeliittas:
"Our [Finnish] Hakkapelites cannot have been any sort of fine representatives. I should mention a parade of the Gustaf Adolf troops in the Thirty Years' War, while the king still lived. At first went the blue, yellow, green etc. mercenaries of the regiment in their flashy gear. Then came, clothed so-so, bridles and baldricks repaired with birch bark and cord, legs hanging from the backs of their small, shaggy horses, cutlasses dragging on the ground, a troop of hollow-cheeked but stern-eyed men. When the Dutch ambassador inquired who they were, the last rider, a fat German Quartermaster [kuormastovääpeli] in charge of the cargo proudly replied 'The royal Life Guards: Finnish, pärkkele!'"
I decided that their coats would be gray (as this is usually the color associated with Finnish troops). Most likely they wore whatever they had available, but I like to paint my 30 years war miniatures in uniform mostly due to convenience. This would represent also undyed woolen clothes. The horses are painted to resemble the Finnhorse, but given that the horses the Hakkapeliittas used were more in the size range of modern ponies, the WG horses are a bit too large. Still... can't have everything.
For the flag I chose the "came with the box" flag of Karberg's regiment, that deriving from the flag belonged to Åke Tott's regiment. The main reason for this is that I'm planning on making Torsten Stålhandske as one of my cavalry generals, although I haven't yet decided which mini I'll be using. Åke Tott was the Finnish-born cousin of Gustavus Adolphus and Torsten Stålhandske (born in my home town of Porvoo) was one of his commanders. Given that Stålhandske was a famous Hakkapeliitta commander I thought that making my troops belong to Tott's regiment was a safe bet.
The problem here is that Stålhandske served in Tott's regiment until 1629 when he was promoted to lieutenant colonel and was leading then the Hakkapeliittas from Åbo [Turku], Nyland [Uusimaa] and Karelen's [Karjala/Karelia] regiments in Breitenfeld in 1631 - I just have no idea what their flags would have been like. The Karelian coat of arms dates from 1562, so that's one possibility, the Uusimaa historical province's coat of arms also dates from the 16th century, and the coat of arms from the historical province of Finland Proper [with Turku as the capital] dates from 1560. Perhaps I'll just make a new one of my own with the Uusimaa coat of arms later on when I get inspired.
edit: I found one source that could provide a good clue to find the "real flag" - Finnish only I'm afraid.
As a quick professional note, the cause of death for Åke Tott has been depicted as "blood surge" (verensyöksy) and it's an umbrella term for various medical reasons. Given that he died rather quickly on road from church to home, the amount of blood lost must have been massive. "Blood surge" usually is understood to be either blood coughing or vomiting from late tuberculosis, intestinal cancer, severe stomach atrophy or intestinal blockage (from Finnish wikipedia), but given his quick death, I propose the actual cause of death to be rupture of esophageal varices, which is both dramatic and can cause death extremely quickly.