2-ME is a reducing agent that helps scavenge free radicals from the medium that are secreted by cells when in culture for a long-time. It also helps cystine transport thus making cysteine more available to cells.
2-ME is however not required for 5-6 h cultures. When culturing splenocytes for 24 h or longer 2-ME is important along with pH stabilizers, non-essential amino acids, sodium pyruvate, L-glutamine and obviously FBS.
Siddhartha is correct. 2-mercaptoethanol is a reducing agent added with the intention of attenuating free radical damage. However, 2-ME is labile and degrades rapidly.
Alternatives are available: dithiothreitol (also labile) and cysteine.
I recommend you some background reading. Have a look at the ATCC, Life Technology, Invitrogen, Corning or Sigma-Alrich web sites.
Ian Freshney's "Culture of Animal Cells" is the bible!
I am thankful to all of you for answering the question. As 2-ME used to denature protein there must be some limiting factor or optimal amount/concentration that should be used.