Would an exoplanet without axial tilt have no seasons?
There are several factors that cause seasons. In approximate order from least to most speculative:
- Axial Tilt: This is by far the significant factor in determining what the season is on Earth. As you may know, axial tilt affects the seasons because the light is "spread out" when it falls on an angled surface. Note that tilt causes different seasons in different hemispheres. An untilted planet could still have seasons for any of these other reasons.
- Eccentricity: The Earth's orbit is very close to circular, so eccentricity has next to no effect on causing its seasons (and in fact, IIRC, currently Earth's eccentricity's tiny effect is actually opposing its seasons). An exoplanet with a high eccentricity could easily have planet-wide seasons due to varying distance from its sun.
- Star Systems: As a commenter mentioned, another factor might be how many stars a system has. If such a solar system is stable (which, surprisingly, it might be, although I can't find the article at the moment), you could get seasons depending on where the stars are in their mutual orbits. A binary star system, for example, would have periods of winter when the stars align with the planets (so one blocks the other) and periods of summer when the stars are side-by-side.
- Star Variation: (From a comment): believe it or not, the sun actually has "seasons" (here) that are on the order of a decade or so. These don't have much effect on Earth's climate since on the sun they mainly cause magnetic disturbances, but on an exoplanet the star's magnetic disturbances could be relatively larger, which would lead to significant temperature/brightness variations that would translate into seasons.
- Internal Energy: Planets could have varying/cyclic sources of energy within them, just like solar masses. In our own solar system, Jupiter's seasons are partly due to this. On a terrestrial planet, variations might come from, for example, volcanic activity. Negative feedback loops of this sort will exhibit oscillations. These sorts of changes might not count as "seasons" for you, though, as they occur over larger timescales.
- Stored Energy: Earth's seasons are complicated by the oceans, which greatly affect the intensity of the seasons, especially in the Americas. In particular, there are various cycles that work like subseasons underlying the main ones. The Pacific Decadal Oscillation, for example, affects seasons years apart. I don't see why an exoplanet couldn't have similar cycles that, unlike in the case of Earth, are the main factor in determining seasons. This could be stored gravitational energy too; for example in a tidally-locked exoplanet/moon system.
If you mean a true Earth-like analogue (in the sense of being exactly-like-Earth-in-every-way-except-the-axial-tilt), then no--it would not have noticeable seasons, since none of the above factors really apply.
*"Any negative feedback loop will exhibit oscillations"* - Not all negative feedback - only feedbacks where the rate of change (or higher derivative) of a variable is related inversely to the variable itself (e.g. spring acceleration is inversely proportional to distance stretched).
Earths eccentricity only opposes northern hemisphere seasons. It amplifies those in the southern hemisphere by the same small amount. IIRC Mars has an orbit eccentric enough that it currently dominates over axial tilt in generating seasons.
@naught101: Close; the dynamical system needs to be C0, have a nonvanishing second derivative on a nondense subset of its input, and be either undamped or else underdamped and forced by a different process. I made this simplification because it is _immensely improbable_ that negative feedback cycles we'd could observe wouldn't be.