Remember, eccentricity is not inclination. You are getting your terms mixed up.
The eccentricity of our planet's orbit is mild; aphelion and perihelion differ from the mean Sun-Earth distance by less than 2%. In fact, if you drew Earth's orbit on a sheet of paper it would be difficult to distinguish from a perfect circle and that is with e = 0.0167. As for a perfect circle, there never will be a perfect circle with the orbital elements. Remember the other planets are also "tugging" on each other.
And indeed tidal lock is the reason the Moon keeps one side to the Earth.
As I said previously, The Earth's rotation is slowing down as well.
We see a number of tidally locked systems within the solar system. Often this invloves more than two bodies.
A more in depth discussion of tidal locking since the Moon is tidal locked to the Earth. The reason the Moon keeps one face to the Earth (Its rotation on its axis matches the period of its orbit) is it is tidally locked to the Earth. Here is a more in depth explanation. The total angular momentum of the earth moon system, which is spin angular momentum plus the orbital angular momentum, is constant. (The Sun plays apart also) Friction of the oceans caused by the tides is causing the Earth to slow down a tiny bit each year. This is approximately two milliseconds per century causing the moon to recede by about 3.7 centimeters per year. As the Earth slows down, the Moon must recede to keep the total angular momentum a constant. In other words as the spin angular momentum of the earth decreases, the lunar orbital angular momentum must increase. Here is an interesting side note. The velocity of the moon will slow down as the orbit increases.
Another example of tidal locking is the orbit period and rotation of the planet Mercury. What is interesting about this one is that instead of a 1:1 synchronization where Mercury would keep one face to the Sun at all times, it is actually in a 2/3:1 synchronization. This is due to the High eccentricity of its orbit.
There also can be more than one body “locked” to each other. Lets take a look at the moon Io. Io is very nearly the same size as the Earth’s moon. It is approximately 1.04 times the size of the moon. There is a resonance between Io, Ganymede, and Europa. Io completes four revolutions for every one of Ganymede and two of Europa. This is due to a Laplace Resonance phenomenon. A Laplace Resonance is when more than two bodies are forced into a minimum energy configuration.
There are also examples of tidal locking in the asteroid belt.
First, the asteroid belt has an estimated total combined mass of less than 1 tenth of the Earth's moon. Second, Jupiter has a profound effect on the asteroid belt.
Since Jupiter has a semimajor axis of 5.2 AU (I AU is the distance from the Sun to the Earth) it ends up with an orbital period of 11.86 years. Since the asteroids are not all at the same distance from the sun, there orbital periods will differ in a direct relationship to their distance from the sun. This will result in some of them having an orbital period of one half of Jupiter. This puts those particular asteroids in a 2:1 orbital resonance with Jupiter. The result of this resonance is gaps called Kirkwood's gaps. The rub is why did not this asteroid belt form a small planet? The reason is the gravitational force of Jupiter. It perturbs the asteroids giving them random velocities relative to each other.
Another effect of both Jupiter and the Sun on the asteroid belt is a group of asteroids that both precede and follow Jupiter in its orbit by 60 degrees. These asteroids are known as the Trojans.