No, but multiple monitors will make your job a lot easier.
If you are trading using a direct access broker and level II software, you will need at least two monitors – possibly even three. When you are trading currencies, on the other hand, you might get away with just one (even though I recommend more); possibly a 21″ LCD (flat screen) or greater. The reason for this is that currencies are a lot simpler to trade, since you only have a few major currencies to deal with.
The software to trade currencies is also a lot simpler than that for stocks. This makes it a lot easier on the budgets of traders that don’t have a significant amount of capital to begin with (the majority of them).
My opinion is that if you can easily afford two monitors to trade, get them. I currently use two additional 23″ LCDs and a laptop myself (I have the same hardware setup at the office and at home for redundancy) – so 3 screens in total. For some reason, I have always used 3 screens. If you want more, go for it!