Some time ago, I was involved in a live action role-playing organisation, eventually leading it. Mostly people made their own padded weapons, but we also had some standard broadswords made up for monsters, casual players etc. I will present plans for both the standard broadsword, some of the more notable player-made weapons, and some important things to avoid...

Instead of dowel or rattan, we typically used a fibreglass rod for the 'spine' of the sword. This material was intended for use in agriculture as fenceposts, particularly for electric fences and where strength was not as desirable as boundary marking (plus, light farm machinery such as quadbikes could roll right over a fence and it would stand back up). It was available in yellow 7mm diameter or white 10mm diameter gauges, and lengths rarely exceeded 1.5m off the shelf.

NB: Care must be taken when cutting fibreglass, with regard to the nasty glass and epoxy particulate that results - you don't want to handle or breathe powdered glass. Cutting underwater or in oil may contain the particulate, but I cannot recommend cutting fibreglass in general. Fencepost lengths are usually about right for swords...

The first step is usually to pad up the tip of the rod with a bit of closed-cell foam and some duct tape. following this, the shape of the blade is cut out from more closed-cell foam - sleeping mats may be your best source of this material. Standard broadswords were made with two identical shapes, outlines matching the outer edge of the blade, and sandwiched over the rod (the rod was taped to one side). This made a heavy, thick sword that was fairly durable and mostly safe. Player-made swords evolved to contain the rod within the layer of foam (ie; a U-shaped bit of foam with the rod filling the space) and featured a thinner layer of foam on the flat of the blade, plus a decent layer of tape. As the aerodynamics of this design are better than round (tube foam over dowel) or double-thick foam as in the standard broadsword, flat-blade strikes were rare, although a bit painful. The important thing is to ensure that the rod is securely held inside the foam, as the foam will bend on impact and a potential to be struck with the rod itself is always present (no different than with dowel or rattan in that respect). All swords were then taped up with silver duct tape, and hilts added. Naturally we had our share of extremists who had to make weapons that were a bit, well, different. Carved closed-cell foam featured prominently, as did the tubular foam mentioned elsewhere (mostly on pole-arms). One madman had a foam-spiked basket-style hilt, with a morning-star made from a tennis ball and more foam attached by string to the hilt... which got disconnected pretty swiftly as there's not much you can do with a reverse-handed chain weapon. That particular weapon was also our first to incorporate tinted latex instead of duct tape (sacrilege!). Naginatas also featured, as did staves and short- or paired swords. I had a pair of leaf-bladed swords with double-hilts - they could be held pistol-style or underhand pistol-style and attached via cuffs to the arm to point straight out. Shortswords were usually cored with the lighter 7mm diameter fibreglass rod. A short-handled warhammer with a head made from expanded polystyrene worked well, although it was a bit shorter than every other weapon and was relegated to use by dwarves (of which we had few)...

In short, fibreglass-based and closed-cell foam-padded swords were the order of the day. The materials were robust, easily sourced and versatile - there was even some recycling available, as the fibreglass seldom broke, compared to dowels.