For 2013, the technical regulations do not change much from 2012, since this is the last year of the current frozen V8 engine formula.
In 2014, every team will have to change to a new turbocharged V6 powerplant, and the technical regulation changes are significant. Any 2014 car will therefore have very limited carry-over from 2013. 2013 will therefore be a more expensive year for any team with pretensions to good performance in 2014, as they will need to design a truly new car around a new engine package. Ferrari has already announced that they are forming two parallel design teams with immediate effect; one team to complete the design and management of the 2013 car, and a team to focus 100% on the design of their 2014 car.
There are rumors that several teams (Force India being one team) are looking to change engine suppliers in 2014, but they are trying to conclude deals now, in order to maximize the amount of time that their design teams will have to design the completely new car for 2014.
From 2014, team engine costs will rise for all customer teams, as engine suppliers look to recover the R&D costs of their new engine packages. The current $6-8m a year cost for a customer team looks to rise to anything up to $14-15m in 2014. This is a significant challenge for less well-funded teams. The failure of the RRA initiative has led to a ramp-up of spending across the board in the last 2 years. Mercedes (nee Brawn GP) downsized expecting all teams to follow the RRA rules, but Red Bull and Ferrari did not, so now Mercedes has been forced to upsize its organization to compete.

Ferrari
Fully funded until Ferrari and Fiat pulls the plug.
Awkward: Santander is paying a lot of money as long as Fernando Alonso remains with the team, but this is a "vanity" sponsorship, the Santander CEO is a motor racing fanatic. If he retires or disappears, the Santander money may disappear quickly.
2013 - Alonso and Massa continue as a pair. Massa's main challenge has been learning how to get the best use out of the Pirelli tires. This may or may not be a problem for him in 2013, since Pirelli is changing it's tire construction for 2013, which is actually leading to an increase in car minimum weight.
2014 - Alonso for sure, but whether Massa will continue is open. Rumors persist that Sebastian Vettel has some sort of memorandum of understanding to join Ferrari in the future.

McLaren
Fully funded, stable leadership. Jenson Button now gets to show his mettle as a team leader for the first time since 2009.
Awkward: question marks remain over the future levels of committment from Vodafone.
2013 - The team's cost base rises by at least $8m with the change in their engine supply arrangement with Mercedes. McLaren has to pay for its engines from 2013 onwards. Sergio Perez replaces Lewis Hamilton.
2014 - The one-time cost of a new car/engine solution.

Mercedes
Mercedes is all in on the F1 program. They have a massive stable of engineering leaders, they signed Lewis Hamilton to a 3 year contract from 2013, and Mercedes bought back the 40% stake that had previously been sold to Aabar. Mercedes has retired Norbert Haug and taken on Niki Lauda as a bridge between the race team and Mercedes HQ.
2013 - A new lead driver in Lewis Hamilton. Mercedes expecting all-season competitiveness
2014 - A championship challenge expected.
If a championship is not obtained by 2015, I expect heads to roll and Mercedes to revert to a pure engine supply role.

Force India
Two owners flirting with financial disaster, a driver leaving for Sauber, big promises of investment by an owner whose airline business is all but bankrupt...Force India has some challenges for 2013 and beyond.
2013 - Paul Di Resta, second driver between Jules Bianchi (possibly as part of a Ferrari engine deal for 2014 and beyond) and Adrian Sutil
2014 - Who knows?

Red Bull
Secure until the time when Deitrich Mateschitz decides that F1 no longer supports the brand's marketing goals. Red Bull outspends every other team at present, but has the championships to justify it.
2013 - Sebastian Vettel, Mark Webber

Lotus
Winners again this season, but big question marks remain over funding and ownership. Genii Capital is rumored to be looking to sell a significant stake in the team, but it is difficult to see who would want to take on 49% of a $100+m budget in the current climate.
2013 - Kimi Raikkonen and Romain Grosjean confirmed

Sauber
Effective on a small budget in 2012. Losing Sergio Perez to McLaren at the end of the season, Esteban Gutierrez is replacing him, which would keep the Mexican sponsors happy in 2013 and beyond. Nico Hulkenberg signed as lead driver in 2013 and beyond. Kamui Kobayashi is out of a drive in F1 in 2013.
2013 - Esteban Gutierrez, Nico Hulkenberg

Toro Rosso
Majority owned by Red Bull (with 40% believed to be owned by Aabar), who would probably sell their stake in a heartbeat for the right price. Owning Toro Rosso would have made sense in a true customer car era, when Red Bull could use the same basic car design for 2 teams, but the cessation of the customer car transition in 2009 forced Red Bull to invest a lot of money in manufacturing capability for Toro Rosso to be able to built its own chassis and major parts once more.
Difficult to see why Red Bull would continue to own this team, other than as the incubation academy for the Red Bull driver program, but the program has little to show so far, with only Sebastian Vettel a success (and he was never truly a Red Bull junior driver, Red Bull captured him from under the noses of BMW in 2009). Both 2013 drivers will be under pressure to show good results or go the way of the likes of Brendon Hartley.
2013 - Daniel Ricciardo and Jean Eric Vergne

Williams
A venerable team that roared back this year thanks to the partnership with Renault, a much better car and a win in Spain. The Renault partnership will continue into 2014, so Williams will be well set for the new turbo era. Still looking for a consistent driver, they have promoted Valtteri Bottas to a race seat, replacing Bruno Senna, hoping for more consistent race day performances from both him and Pastor Maldonado. Right now, Williams cannot do without the PDVSA money, but another good season with one or two victories will increase their chances of landing a major sponsor to allow them to hire top-flight driver talent again.
2013 - Pastor Maldonado, Valtteri Bottas

Caterham
A team that is failing to move up the grid, despite a healthy budget and design team. Their need for money is shown by rumors that they will replace Heikki Kovalainen with a pay driver in 2013. This is one of only two open seats in F1 at present, so Caterham has several pay drivers to choose from, including Vitaly Petrov and (possibly) Bruno Senna.
2013 - TBD

Marussia
A money pit (over $100m spent in 2012 alone) with little to show thus far after a painful transition in 2011 from a design process entirely based around CFD to one using both CFD and aero modeling. Unclear who they will use as an engine supplier from 2014 onwards, with Cosworth unlikely to continue due to a lack of customers.
2014 - Timo Glock, Max Chilton

HRT
The team has ceased to exist. Current owners Thesan Capital pulled the plug on the team in December 2012. The team had little in the way of assets, since most of its infrastructure was rented or leased. It did not have the ability to manufacture its own chassis for example. Other teams would be available (see Toro Rosso) that would be far better equipped.