The second most-hated question among statistical and/or computational people (the first being do I need replicates?).
How many replicates you need depends on two parameters:
1) What effect size are you trying to detect, between the experimental groups? (For example, is a fold change of 10:1 all you care about, or do you want to detect a mere 2-fold change?)
2) How variable are your replicates within the groups?
The smaller the effect size (difference between groups) you want to detect, the more replicates you need. The larger the variability within your groups, the more replicates you need. The underlying principle is known as statistical power, and there is no one answer. With two replicates, you might find that some very dramatic changes appear statistically significant, but as Rory said, the statistics will be dubious at best. Three is common, but usually at best barely adequate. Lacking other information, we usually suggest 4, on the assumption that 1 will fail, and the remaining 3 may be barely adequate to give you the magic p<0.05 for some peaks.
I really strongly suggest you consult a statistician at your institution regarding experimental design. You're putting a lot of time and effort into the lab work... a consultation with your local statistics clinic is a very low-cost way of enhancing the likelihood of a good research result from all your effort.
Best of luck,