Measurements of energetic electron beams generated from ultrahigh intensity laser interactions (I>10(19) W/cm(2)) with dense plasmas are discussed. These interactions have been shown to produce very directional beams, although with a broad energy spectrum. In the regime where the beam density approaches the density of the background plasma, we show that these beams are unstable to filamentation and "hosing" instabilities. Particle-in-cell simulations also indicate the development of such instabilities. This is a regime of particular interest for inertial confinement fusion applications of these beams (i.e., "fast ignition").