I usually render most of my images at around 1000x1000 pixels, since i hate really large images going far off my screen. But i notice that a lot of other artists tend to use larger dimensions, like 1400x1200 or 2000x2000 pixels. Other than the increase in size, is there any other benefit to this? Are 2000x2000 pixel images higher quality than a 1000x1000 one? What would be an ideal image size for most poser images?

I would say there is no ideal - depends entirely on what you're using it for!

As an example, say you want to view an image on screen at 1000 pixels at the longest side - rendering twice as large and then reducing the size in an image editor (plus doing stuff like sharpening, adding contrast, altering colour etc to taste) can make a render appear much more detailed (advice I picked up from one of blackhearted's pdf's some years ago). If you're going to add painted effects like hair, smoke etc it also makes it far easier if you start with a large render size.

I usually render at the same resolution as my largest monitor, for use as a background without stretching. The more pixels, the more details are visible in the picture. I often use 1600x1200 since it will fit on most monitors easily and has a TV/old-movie like 4:3 ratio.

Rendering larger will also allow for printing. Sometimes what we see on the screen will be tiny printed out.

I find some forms of postwork are easier on a larger render. Other times, I change my mind about the framing of the subject and it's useful to be able to crop some of the image off and not lose resolution.

Is there a large quality/detail difference between 1600x1200 and 1000x1000? Or are the extra pixels used so that the image is larger length and width-wise.  And if i want to zoom in a bit on a render, is 1000x1000 good enough or do i need to increase my image size?

Render dimensions can also have an impact on the output.

If the shaders are setup to add lots of detail and you render it at 1000x1000 you are doing a lot of cpu math the gets thrown out based on the post filter in use, and the settings.

Sometimes I render things out at 6000+, other times it is to fit certain dimensions.

Yeah. I usually add a softening technique though that adds a bit of blur to my images, so usually those small details get lost anyways. Would 1000x1000 look good on most people's monitors or should i start going to 1200x1200? My preference is square shaped renders rather than the usual 4:3 aspect. I'm doing this just for fun, with no intention of printing anything out or any professional work.