I'd like to play board games with friends who live in other states. I thought I could use Skype to communicate and a webcam to send out a picture of the board. Does anyone have suggestions on how to handle cards that are dealt to different players? For example, if I were playing Risk, how could a player be dealt a Risk card without someone else knowing what card was dealt?
Play by Email (PBEM)
There are lots of board games around which a play-by-email communities have sprung up. This site appears to have a list of hundreds of games that have been adapted to distance play and links to help you get started.
Personally I've played A&A by email over at AAMC.net, which has a entire player ladder, ranking system, and server that logs games and rolls dice (to eliminate the tedium of documenting real rolls and the problem of how to prevent cheating).
Most of these communities have established combat nomenclature for communicating moves and other information to the other player(s)--somewhat akin to chess or go notation. Furthermore, they typically have message boards to help PBEM newbies get started and/or find people to play with.
As you say, it is quite difficult to keep things a secret in this style of play, unless you have a referee who controls the game, and tells you what you can and can't know (just like how a computer would do so in an online version). This isn't much fun for the referee though, as they obviously wouldn't be able to play as they would have total knowledge of the game state!
The best option is to play online, rather than play with the real board game. There are several questions on this site already about good sites to use, but here is a community maintained list of the best resources online for playing games.
For board games, there are many options.
The simplest is the java-client or flash-client website option, tho' it can be hard to meet up your friends in some. Examples include Game Table Online, Brett Spiel Welt, Board Gaming Online, and several others.
A few game companies, most notably Amarillo Design Bureau and Days of Wonder, have their own online play systems for their flagship games. SFBOL and FCOL are both through a separate company but licensed for online play by ADB; both at sfbonline.com; it's a subscription model. Days of Wonder has Ticket To Ride Online, and then fist of dragonstones, queen's necklace, and gang of four as sweeteners. TTRO is pay per module lifetime access (now); it used to be pay for membership and access all for a time-limited subscription.
One recent challenger is Battlegrounds; can't say anything about their software, good or ill... but their list of VTT's for both RPG and boardgames is impressive, if filled with dead links (and marked as such). http://www.battlegroundsgames.com/links.html
Also Boardgamegeek has some games that are regularly played by Forum. One member will usually manage the game state and update players about their secret information via private messages and publish the new state of the game in the forum for all to see.