Would the existance of other cryptocurrencies negatively effect Bitcoins? 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.