Yes it makes a difference. It might be subtle or it might be night and day.
FX are usually Serial - the first one feeds into the next one etc.

Typically if there is a compressor in the chain. It will go last. (to catch any volume changes in the fx before it)
If it's a gate, you might want that first in the chain so that other fx following are not also enhancing the noise.
As far as Verb, echo, EQ etc. It all depends on what you're looking for.
Ex: Eq before a reverb changes the signal going to the verb. - Eq after the verb changes the quality of the verb itself.

But there are no real rules if that's what you're looking for.

Personally, I like to compress first. I would eq after compression because compression is effected by eq and you may find that any adjustments you make in the eq will change the way the compressor reacts. I know some people like to eq before and after but to me this seems counterproductive if not entirely overkill. I'm sure Remy will chime in on that soon.

As far as inserts are concerned, I only use compression, expansion or eq in the inserts. You don't generally want to apply delay or modulation effects to the entire signal and having those types of effects on their own channel gives you more control over their intensity. That's just the way I work. YMMV.

When working in a processor-intensive mix, you can use quality EQ plugs before the compression followed by a less high-quality EQ (such as Cubase' built in EQ) after. This allows you to put, say, a 2k cut with a musical EQ, then repeat the cut afterwards with the 2k band having a proportionately lower effect while still giving you before-and-after control.

Helpful responses all around. Thanks.

Someone showed me that it may be a good idea to do preliminary cutting of the lowest frequencies before a compressor and then do an actual EQ of the instrument/sound after the compressor. They said to do this so the compressor didn't work as hard compressing the low frequencies that we can neither hear nor be produced on most speaker systems. I don't know how much this effects it but it seems logical enough. Just thought I'd put that out there. Feel free to correct my thinking on this one! Thanks,

-Cameron

I typically make this decision based on a few things: the instrument in question, the style of mix and where I want something to sit.

Try this test. Take a lead vocal or drums through a bus and add a quality EQ plug-in followed by a good compressor. When EQ runs into a compressor, the effect of the EQ is more subtle. The peaks created by the EQ are squashed by the compressor (how much depends on your settings of course) causing the audible "effect" of the EQ to be somewhat softer.

On the flip side, try the EQ after the compression. The original signal's dynamics are compressed then shaped by the EQ, causing the the source to gain some punch (drums are a great test for this) and move forward in the mix (vocals love this).

Both approaches have their upside and the source and type of mix are the best gauges of which way to go for me.