Will bitcoin's value be affected by other digital currencies? There are many different digital currencies being released now, following in the footsteps of bitcoin and trying to improve upon it.  Will these currencies, by giving consumers more options, reduce demand for bitcoin and decrease or limit the increase in its value?

Stephen's answer made me realize that I'm not just talking about any crypto but the one's that will inevitably improve upon the already great bitcoin model.
Bitcoin is a "proof-of-work" based cryptocurrency.  Proof-of-work based cryptocurrencies are protected from a malicious 51% attack because of that coin's mining network.

Bitcoin is protected by 12,500 Th/s of mining capacity (using SHA hashes).  For an attacker to come in and attempt to commit "double spend" fraud (as the result of having 51% of the mining capacity), that attacker would need to spend perhaps a hundred million dollars to acquire the necessary mining hardware.  There is no way, today, that an attacker will be able to use this tactic to earn a profit because there's simply no way to withdraw even tens of millions of dollars worth of funds from exchanges (following the attack) -- due to exchanges employing KYC/AML policies such that an attempt would fail either due to withdrawal limits, access to cold-storage, etc.

Alt coins don't have this same threshold.  

So in addition to Bitcoin having first-mover advantage and the strongest "brand" (thus that's why Overstock accepts Bitcoin and not Litecoin or anything else), it has the least risk of catastrophic loss due to a malicious 51% attack.

The difference between Dogecoin and a Bitcoin is like the difference between investing in a longshot penny stock issue of a nearly bankrupt company versus buying a blue chip NYSE which continues to deliver quarter-after-quarter.

So there is certainly a substitution effect.  Many of those speculating on Litecoin would otherwise have been holding bitcoins.  But there's not an easy way to know what the value of a bitcoin would be if the $500+ million valuation of all Litecoins in circulation were to grow by several billion dollars.  Since we haven't reached "saturation", perhaps many of those speculating on Litecoin might not have held Bitcoin regardless -- and thus if that were the case the existance of Litecoin didn't affect Bitcoin's exchange rate.

There's also the situation where an altcoin happened to be the "gateway drug" that caused a person to become interested in crypto currencies but then that person later embraced Bitcoin. In that instance, the greater the traction of that type of person to an alt currency eventually results in greater traction of Bitcoin.

There's also other altcoins that are not proof-of-work based.   For instance, PPCoin is a "proof-of-stake" crypto currency.  These are not vulnerable to a 51% mining attack (though they have other vulnerabilities).  So it is possible that those PoS coins could be seen as having an equal (or lesser) risk to that of Bitcoin and thus that coin could be seen as a substitute for Bitcoin by some.

To conclude, simply alt coins are not equivalent to bitcoin and thus a dollar spent on acquiring an altcoin doesn't mean there is one dollar less spent on acquiring or holding a bitcoin.