In Finland, after the surprising surge by the conservative National Coalition (Kansallinen Kokoomus) in the March parliamentary elections, KOK will be incorporated into the new government. If all goes well in upcoming talks, the government will be formed by Finnish Center (Suomen Keskusta), the party of PM Matti Vanhanen; the Kokoomus; and two smaller parties, the Swedish People's Party (Svenska folkpartiet), which is always in government, and the Greens (Vihreä Liitto). Helsingin Sanomat provides more detail on the coalition negotiations.
One might expect that the new government platform will have something to do with lowering some taxes, increasing competitiveness, and perhaps doing something in the direction of a guaranteed minimum income (giving recipients more flexibility). One question HS brings up is what position will be awarded to wildly popular Sauli Niinistö, the 1994-2001 party leader and '06 presidential candidate (who almost defeated incumbent Tarja Halonen and relegated PM Vanhanen to a distant third). Niinistö served as finance minister in both Lipponen SDP-led governments (1995-2003), but that post apparently will go to current party chair Jyrki Katainen. Possiblities include foreign minister or speaker of the Eduskunta. (Apparently, the latter is a fairly prestigious position; the previous holder of the office was ex-PM Lipponen himself).
Governments in Finland tend to be supermajorities so that no small party can hold the coalition "hostage." The last government, KESK+SDP+SFP, met this criteria as Keskusta and SDP together held 108 of the Eduskunta's 200 seats. This time, KESK and KOK together hold 101 seats, a razor-thin majority; SFP holds 9, and the Greens 15, giving the coalition a total of 125 and not allowing either Greens or SFP to hold out on any particular issue.
SDP leader Eero Heinäluoma has criticized the Greens for participating in the government; this really just seems like sour grapes, especially before a platform is out. Hence we will have to see what comes of the negotiations. (Who knows... maybe the notorious Vanhanen's purported liaisons with a Green MP had something to do with it? Don't take my word for it, check out all these links in Finnish I can't read).
Meanwhile, in Estonia
The Center Party (also KESK, since Estonian and Finnish are family members) has been kicked out of government in the new post-election scenario. The new government (already sworn in on 5 April) seems rather awkward at first glance, incorporating the conservative Pro Patria/Res Publica Union and the Social Democrats as well as the free-market Reform Party of PM Andrus Ansip.
I have absolutely no idea what has led to the formation of this government, and the only suggestion I would have is that perhaps the Center Party's reportedly more pro-Russian (perhaps better to say less anti-Russian) stance got it booted from government, along with personal rivalries and the close finish between Center and Reform. This was probably more galling for the Center Party, which had the most seats of any party in the previous coalition; Reform surged ahead of Center to become the largest party in parliament. Hence electoral calculations (rather than policy) may have played a role, though that's pure conjecture.
As far as policy goes, it appears the government will cut the flat tax from 22 to 18 percent. The new government also reiterated its determination to remove the Soviet war memorial from Tallinn.
Update: This blog has a lengthy analysis of the Estonian government formation.