Would the existence of other cryptocurrencies negatively effect Bitcoins? It seems that other forms of cryptocurrencies would be competition to Bitcoins. Alternately, would it be like having other currency units like real money where the English pound and US dollar do not compete?
It depends a lot on the circumstances. If the use cases overlap significantly, then the currencies can compete. That could negatively affect Bitcoins. However, if the use cases don't overlap significantly, then the currencies likely won't compete. That could even positively affect Bitcoins.
Crypto-currencies aren't fighting over shares of a fixed-sized pie. Crypto-currencies are cooperating to enlarge the pie and bring their benefits to a much, much broader population.
In my opinion, near clones like Litecoin do affect Bitcoin negatively because they don't attract a new population and they do reduce the chances that Bitcoin will attain critical mass. However, I must stress that one shouldn't assume that anything that's bad for Bitcoin is bad for mankind. It's always possible a new crypto-currency will come along that's much better for humanity than Bitcoin is, and the weaker Bitcoin is at the time, possibly the better for that currency. Of course, on the flip side, the more Bitcoin has paved the way, perhaps the better for that currency.
There is the theory first described by Hal Finney that if an alt currency supplants bitcoin (in which Bitcoin's value goes down as coins are sod for transfer to another) then that is something that too can be repeated over and over, and thus crypto currencies lose their ability to be a good store of value.
So that happening harms, over the long term, not just bitcoin but all crypto currencies.
But Bitcoin is a proof-of-work (POW) based crypto currency, and thus it is susceptible to a 51% attack. Thus it needs a sufficient level of hashing for the network to be protected. This is what differentiates bitcoin from competing POW-based crypto coins which have a hashing capacity just a tiny fraction of Bitcoin's.
But there still could be multiple successes, since all that needs to remain protected from a 51% is sufficient hashing capacity and there might multiple POW currencies with a sufficient level.
At this moment, Litecoin may not yet have a sufficient level but it is the closest to Bitcoin to reaching that state.