I was looking at various planes, and was wondering why we don't have oval shaped fuselages instead of only round ones. Is there a reason? Perhaps aerodynamics, or stresses?
TL;DR: There are (primarily structural) reasons for circular fuselages... but there are also reasons to deviate somewhat from circularity, and many aircraft actually do have oval fuselages!
(Explanation partially cribbed from here.)
For a pressurised aircraft, a circular cross-section is indeed optimal from a stress standpoint, as it spreads out the pressurisation stresses evenly without any areas carrying a much higher stress than others. Areas of high pressurisation-stress concentration are bad, because pressurisation imposes cyclical stresses (each time the aircraft takes off and ascends to cruising altitude, the pressure differential between inside and outside gradually increases,1 imposing increasing stress on the pressure hull; each time it descends from cruising altitude and lands, the pressure differential gradually decreases, eventually to zero, slowly releasing the stress on the pressure hull), cyclic stresses produce fatigue damage (something to which the aluminium alloys generally used in aircraft construction are unusually vulnerable), and fatigue cracks tend to start in areas of concentrated stress. Additionally, if the fuselage has a non-circular cross-section, then the pressurisation stresses will want to deform it into one with a circular cross-section (as a circle has the greatest enclosed area of any closed shape with a given perimeter, and, thus, a cylindrical fuselage - i.e., one with a circular cross-section - has a greater cross-sectional area [and, thus, volume for containing pressurised air] than any fuselage with a non-circular cross-section), producing bending stresses in the fuselage - another way in which a non-circular-cross-section fuselage promotes fatigue damage.
However, a circular fuselage often isn't the best shape when you start wanting to put stuff in the aircraft, since the way the walls curve inwards as you go up and down can make it hard to put seats or cargo near the edges of the cabin. Many pressurised aircraft, especially large pressurised aircraft, do have circular fuselages (as large-diameter fuselages have a lesser degree of curvature than small-diameter ones, causing this disadvantage to be less prominent), as seen (for instance) on the 777 and 787, but many others (especially smaller aircraft) use non-circular fuselages. One way of doing this is to use a fuselage cross-section shaped like two overlapping circles (the Boeing 377, a.k.a. "Stratocruiser", is a spectacular example, but other aircraft, such as the DC-8 and DC-9, also use this method, although much less noticeably). This produces a cross-section with a pronounced cusp at the intersection of the two circles; this would seem like it should create insane fatigue problems, but almost all of the stress concentration at the cusp is eliminated by stringing the floor between the two cusps to act as a tension brace, and the minimal amount that remains (due to the slight differences in mechanical properties of the hull and the floor) is easily dealt with by slightly thickening the skin around the cusp.
Another way is to make the fuselage taller than it is wide, decreasing the curvature of the cabin sidewalls while increasing the curvature at the very top and bottom of the cabin, and ending up with a fuselage that is... [drumroll] oval in cross-section! Some aircraft (such as the A380) do something distinct but quite similar, where the upper fuselage is stretched vertically but the lower fuselage is not (in order to keep the floor of the cargo hold flatter), resulting in an egg-shaped fuselage cross-section:
(Image by EADS, via EADSpics [since taken down] at Flickr, via @aeroalias here at AvSE; the noncircularity of the A380's fuselage cross-section is especially prominent due to its having two passenger decks stacked one atop the other, requiring more vertical space than for a single-passenger-deck aircraft, but a great many pressurised single-deckers also have oval fuselages - just less-obviously-oval ones.)
Both the oval and the egg have the disadvantage of producing stress concentrations in the curvier parts of the fuselage, but this is easily dealt with by using thicker skin panels, and, potentially, more rivets, in these areas. (The floor[s] tying the two sides of the fuselage together probably also help by acting as tension braces, just like for the cusped fuselage.)
1: If you want to be really pedantic, the aircraft doesn't pressurise as it ascends. The pressure inside the aircraft actually decreases on ascent, up to a cabin altitude2 of 8,000 feet or so; however, the ambient pressure outside the aircraft decreases much more quickly, so the pressure differential between the interior and exterior of the aircraft does build up as the aircraft ascends. This has exactly the same effect on the aircraft's structure as if you left the aircraft on the ground and pressurised it by pumping in more air - the structural stresses imposed on the aircraft don't care if the pressure differential is produced by increasing the pressure inside the aircraft or decreasing the pressure outside the aircraft.
2: The cabin altitude is the altitude at which the ambient atmospheric pressure (assuming a standard atmospheric-pressure profile) would be the same as what the pressure inside your aircraft is now. For instance, if the pressure inside your aircraft's pressure cabin is the same as the pressure one would experience floating at 5,000 feet above mean sea level with no aircraft, your aircraft's cabin altitude is 5,000 feet.