What a difference a few months makes...it seems like only yesterday that all of the predictions in F1 were for a reduction in the number of teams. Minardi and Jordan were both reckoned to be living on borrowed time. The fear was that the remaining privateer teams would leave the sport, leaving F1 dominated by the motor manufacturers and Ferrari.
Now, since the news that Jenson Button had managed to buy his way out of his contract with Williams for 2006 and 2007, which left Honda with a problem called What To Do With Takuma Sato, it seems that every other rumour is about a new team. So far in the last 3 weeks we have been treated to the following speculation about new teams:

The Honda "B" team (Sato plus Davidson), to be run out of the old TWR factory at Leafield
The McLaren/Mercedes "B" team (aka Team Dubai), with Jean Alesi rumoured to have a management role

Additionally, there are persistent rumours that Coca-Cola is looking to enter Formula 1 in the near future, and just about every team in the pitlane has been connected with them in the last few months (although one would think that any team owner would give his right arm to have them as a sponsor, so a lot of the talk may be wishful thinking).

Why, within a few months of all speculation pointing to a reduction in the number of teams, are we now looking at an economic boom in the sport? The world economy is not booming right now, so what is the underlying reason.
The underlying reason may be the power struggle between teams supportive of the FIA (the leader of which is Ferrari) and teams supported by the automobile manufacturers. In recent months, the position of the FIA teams has been strengthened considerably. Red Bull racing signed to use Ferrari engines in 2006, which gave the FIA 2 teams. Then Red Bull agreed to buy Minardi, which gives the FIA a third team. Williams still has no long-term manufacturer partnership after the termination of its relationship with BMW, so they might be persuaded to switch camps. That would give the FIA 4 teams.
The manufacturers needed to respond to this by increasing the number of teams that they support. Toyota already supplies a second team (Midland), making them the only manufacturer to do so. Other manufacturers needed to step up to the plate. Honda now have an excuse to run a second team since they have to keep Takuma Sato gainfully employed.
The manufacturers recently met near Munich at the end of September to discuss their next moves. They issued a statement which was predictably content-free, containing the usual puff-phrases - the sort of statement that is more notable for what is not said. Predictably, there was no public comment about manufacturers supplying more teams with engines.
Other manufacturer-supplied teams may appear in the next 2 years as the manufacturer faction seeks to shore up its position against the FIA, and also as a way of covering at least some of the cost of developing and building V8 engines, which have driven up engine supply costs when they were supposed to reduce those costs. (Unless the teams can be persuaded to dramatically reduce testing, which consumes most of the engines used in F1, engine costs are sure to continue to be exhorbitant).
I therefore believe that the new teams will be mostly funded by manufacturers as part of the ongoing power struggle.