What's an easy to use juicer that juices oranges as well as other fruit?

I like the OXO good grips citrus juicer. It has a reamer for fruit the size of orange which flips over for smaller fruit such as lemons. I think it beats a wooden hand reamer because it holds the juice and filters out seeds. No peeling is necessary. It's manual, but I think that is easy.

The problem you are presenting is that "all fruit" that can be juiced covers a lot of ground. Nearly all fruit has some parts that need to be discarded, but it varies by fruit. As you noted, for oranges (and grapefruit, and lemons, and tangerines) it is the peel. For apples and pears, it is the peel and the core. For apricots and peaches, the pit. And there are some basic differences in juices. Do you want pulp, or do you not want pulp?

Assuming that the "all fruit" is more important than the "not peeling" I'm going to recommend either a Vitamix (or other hard-core blender style) if you are OK with pulp, and the spin extraction style if you do not want pulp.

I have had a Vitamix for years and years (good durability) and you can clean them by half filling the container with water and a bit of soap and just run it (easy to clean). You need to do the basic peeling of citrus, although it is fine to leave some of the pith, and you only remove the seeds/core of the apple or the pit of the peach. The skin just becomes part of the juice. The juice is closer to a nectar in thickness and is thick, rich and delicious. But it is pulpy. I consider that a good thing, but you may not.

The juice extractor requires the same first steps as the Vitamix (although some will allow you to leave the apple core and seeds) but uses a grinder and then centrifuge method to force the juice through a sieve and into the waiting receptacle. You get a pretty clear juice, but are left with a heck of a clean-up, and a bunch of pulp to compost or feed to your chickens.

Basically, you have two types of fruit for juicing: Those with a rind (lemon, orange, grapefruit) and those without (strawberries, grapes, apples, etc).

Non-rind fruits: Wash and use a vitamix (blender). Turn it into juice and pulp. If you don't want the pulp, pass it through a sieve or chinois.

For citrus, the best juicer I've used are the manual press type juicers. They are easy to clean, easy to use and don't produce any bitter taste. They can be a little large though.

The electric juicers are popular, but you can't easily wash all of it, they are easy to burn out (any water in the motor will destroy them), they're expensive, and most importantly, the harder you press, the more bitter taste of extract (from the pith).

In a pinch, use a fork.