Tris buffers are used under slightly basic pH conditions, as for DNA electrophoresis, because this keeps the DNA soluble in the solution and deprotonated so it will be attracted to the positive electrode and will migrate through a gel. EDTA is an ingredient in the solution because this common chelating agent protects nucleic acids from degradation by enzymes. The EDTA chelates divalent cations that are cofactors for nucleases that may contaminate the sample. However, since the magnesium cation is a cofactor for DNA polymerase and restriction enzymes, the concentration of EDTA is kept purposely low (aroun 1 mM concentration).
Although TBE and TAE are common electrophoresis buffers, there are other options for low-molarity conductive solutions, including lithium borate buffer and sodium borate buffer. The problem with TBE and TAE is that Tris-based buffers limit the electric field that can be used in electrophoresis because too much charge causes a runaway temperature.