The last collider like this was the LEP, "Large Electron Positron" collider, at CERN. It had a maximum energy of 100 GeV per beam, and was decommisioned in 2000 to make room for the Large Hadron Collider, which now occupies the same tunnel.
There are proposals for an ILC, "International Linear Collider", which would have an energy of 500 GeV or possibly 1 TeV. Also CLIC, "Compact Linear Collider", which might have a still higher energy in the 3 to 5 TeV range. Mainly, all such plans are on hold until results from the LHC indicate whether building such a machine would be justified.
Colliding electrons is not so much different from colliding protons. In both cases you get debris consisting of "everything", although in different proportions. The big advantage is accuracy. High energy proton collisions are in reality collisions between two quarks, and since quarks oscillate violently inside their protons, the energy of the collision is not sharply determined. When colliding electrons you know the energy.
The disadvantage is that it's harder to accelerate electrons, since they radiate so much synchrotron radiation. You need to use linear colliders rather than circular colliders to reduce this.
All the things being studied by the LHC, including Higgs, could be studied further by these machines.