Accurately representing the orbits of all the planets in a single image is very difficult. There are really two solar systems: the inner system (Mercury through Mars), and the outer system (Jupiter through Pluto). If you draw the outer system to scale, the inner system is reduced to a bunch of tiny, almost overlapping ellipses crowded near the Sun. (That's why it's so difficult to launch probes to the outer planets, and why they take so long to get there.) As an example of the grand scale of the outer solar system, consider the eccentricity of the orbit of Pluto. The difference in the distance from Pluto to the Sun between Pluto's perihelion and aphelion is almost twenty times the total distance from the Earth to the Sun!
The orbital path of comets with extremely elongated elliptical orbits (eccentricity close to 1), parabolic, or hyperbolic orbits cannot be shown in their entirety (parabolic and hyperbolic orbits are theoretically infinite in extent). Orbits of such comets are tracked to beyond the orbit of Jupiter, following both the inbound and outbound legs of the orbit.
Over the centuries, artists depicting the solar system and designers of mechanical orreries have resorted to a variety of dirty tricks to get around this problem of scale, and Solar System Live implements most of them. First of all, you can choose to display either the entire solar system or just the inner system. When you display the entire system, the inner planets will be all mashed together (except if you select Equal mode for orbit plotting), but even though the discs may overlap you'll usually be able to see the relative longitudes around the sun. When you're interested in the details of the inner system (for instance, whether an opposition of Mars occurs at perihelion or aphelion), simply check “Inner” to display only the inner solar system.