Eccentricity matters little (at least for Earth).
The eccentricity of Earth (e~0.0167086) means that the planet orbits in an ellipsoidal path that is 147.1 million kilometers away from the sun at its closest and 152.1 million kilometers away at its furthest (the maximum is 3.4% larger than the minimum). The energy output of the sun (as a blackbody radiator) is proportional to the Sun's temperature of approximately $5800K-6000K$ at the surface, which results in a power output of approximately $4.0×10^{26}\ W$. If we want to know how much solar power hits earth we typically look at the Watts-per-square-Meter Earth recieves. At a certain distance $r$ from the sun, the power per surface area is proportional to:
$$
P_{total}/A_{total}=P_{total}/(4\pi r^2)
$$
If you plug in the numbers for $P_{sun}$ and both $r_{min}$ and $r_{max}$ you'll get the following values:
$$
1471.04\ W/m^2 \ (at \ minimum \ distance)\\
1375.92\ W/m^2 \ (at \ maximum \ distance)
$$
and notice that that is a total change of less than 7%, which doesn't seem like nearly enough difference to cause sweltering summers and freezing winters in so many different places on Earth.
Furthermore, if summer were caused by being closer to the Sun, then every continent should experience summer at the same time. However, the Northern hemisphere experiences winter in December while the Southern hemisphere has summer in December. So what is going on?
Obliquity matters a lot.
The Earth is tilted on its axis by $23.5^{\circ}$. The axis points toward Polaris (the North Star) throughout the year, which means that during part of our orbit the Northern hemisphere will be tilted a little more toward the Sun, and during the other half of the year the Southern hemisphere will be tilted more toward the Sun. However, we already know that distance changes don't change the $W/m^{2}$ received by much at all when we look at orbit changes, and orbital tilt is only going to change distances by a much smaller amount that eccentricity, so what is going on?
Direct sunlight is the key. Sunlight bounces off Earth's atmosphere very similarly to how it bounces off the surface of a lake or ocean. If you look straight down into the water very little light is reflected off the surface and you can see into the water. But if you look out across the water a lot of sunlight is reflected and you mostly see reflections rather than seeing into the water. This is exactly what happens to sunlight hitting the Earth's atmosphere. In December, the tilt of the Earth places the Southern hemisphere into the most direct sunlight and very little is reflected off the atmosphere (just like very little reflects of the surface of a lake when we look straight down). However, the Northern hemisphere is tilted away and which means the angle of the sunlight relative to the surface of the atmosphere is much less direct. Therefore, just like more sunlight is reflected when we look out across a surface of water, more sunlight will be reflected by Earth's atmosphere when the Sunlight is less and less direct.
What does that all mean?
It means that fictional spacefarers or worldbuilders will have to be careful in choosing (or designing) their new Earth-like homes.
A planet with no tilt and no eccentricity will have no seasons (barring other factors). Such a planet will be warmest at the equator where the sunlight is most direct, and will get colder and colder as latitude increases (as more sunlight is reflected at less-direct angles).
If the planet's sun delivers a similar $W/m^{2}$ as Earth, then the equator will be absolutely sweltering (even in comparison to Earth's). The Arctic will be colder, never getting a warm season, and so permafrost will extend to lower latitudes than we have on Earth. This means that the amount of land with comfortable living conditions will be centered mostly on the middle-latitude bands. (Assuming variety of landmass/oceans is similar to Earth and not some perfectly-designed masterpiece extending habitable zones by ocean currents, etc.)
Following similar logic a low-$W/m^{2}$ planet would push the habitable zones closer to the equator, and a high-$W/m^{2}$ planet would push the habitable zones closer to the poles.
A planet with no tilt and high eccentricity could have seasons based on orbital $W/m^{2}$ fluctuations, but the orbits would have to be quite eccentric to create large temperature differences since the $W/m^{2}$ changes proportional to $(r_{max}/r_{min})^2$.
It is also notable that Winter/Summer cycles wouldn't be very symmetric in this sort of situation. Very eccentric orbits would lead to very short hot summers and long cold winters.
A planet with Earth-like tilt and no eccentricity would be very Earth-like.
A planet with Earth-like tilt and larger eccentricity could be very Earth-like, depending on which way the tilt is pointing. (In other words, tilting-in at the minimal radius could make summers really scorching hot and the long cold winters colder for one hemisphere, but tilting-in during fall/spring would be pretty good.)
Any world-building contractors can make their worlds have seasons by tailoring the tilt as they see fit. Furthermore, why design spherical worlds when a cylinder-shape will tilt everyone to the same angle at the same angle at the same time (no more Southern/Northern hemisphere seasonal differences)
