Wareg: Thanks. You're entirely right to correct me there, as you say, the Swiss relied on the halberd initially.
Plumo: Yes, mercenary longbowmen should certainly be available to the Flemish. While I'm not sure the 14th century counts deployed them, that was in part because they sided with the French in the HYW, and the Burgundian dukes (while counts of Flanders) often used them.
lolIsuck: The Brabanšon knights are a bit of a mixed bag. In the 13th century they were quite good, as demonstrated at Worringen, but the 14th century was rather a disaster for them, as they were defeated many more times than they managed to win, for example at Scheut (1356), Baesweiler (1370 iirc), Grave/Ravenstein (1388 iirc), every time they were up against a comparable foe. In the 13th century they had managed to defeat almost singlehandedly a coalition with Guelders, Cologne, etc, while in the 14th century they could not defeat solitary Guelders with the assistance of the kingdom of France! They had to be bailed out by the duchy of Burgundy, and even then they could only maintain the status quo. The only real victories they achieved were against rebellious vassals and the like, such as the lords of Valkenburg, who were certainly no equals.
As to other mercenaries originating from the Low Countries: there was a very considerable movement of settlers from the Low Countries to Central/Eastern Europe. These also appear in the Kingdoms Teutonic campaign, I believe, as Burgher Infantry (or some such). This is true: the colonial cities founded were populated with many Dutch settlers as well as Saxons. There were about 200 000 of these altogether. These could be represented by some kind of militia or mercenary unit.
I believe it's been mentioned before, but the Flemish were also widely employed as mercenaries by the Normans. They participated in the Norman invasion of 1066 and also came as waves throughout the 11th and 12th centuries (again, as with the Brabanšons, the term may be a generic word for anyone from the Low Countries, not just those from the county of Flanders). Gerald of Wales mentioned that they were not just colonists - particularly active at weaving - but could fight just as easily. They had their presence mostly in Southern Wales and Southern Scotland - areas of Norman encroachment, where the Flemish were used as support for the reigning Normans. So they could be some kind of militia/mercenary crossover perhaps.
Apart from that, the Frisians were the most distinctive of Low Countries soldiers. Not always fully disciplined or equipped, but inventive and persistent. They participated in the siege of Lisbon by the Christians as well as in the Holy Land. They also supported the attempt of Willem II, king of the Romans, to become emperor, and participated in his sieges (for example of Aachen) in the 1250s. In the 14th and 15th century they became more prone to piracy and civil war. Like the earlier mentioned troops, they would be best served as infantry. This is a recurring feature among Low Countries warfare - the terrain just wasn't ideal for horses.
The only two exceptions would be the more cavalry-oriented Brabanšons (that is, the army of the dukes of Brabant, not the Brabanšon mercenaries) and Guelders. I would consider the latter a more successful cavalry-based army. They were also used as mercenaries, although particularly on a local level. They fought for the Burgundians and participated in the civil wars after the deaths of Charles the Bold and Mary of Burgundy.