OK I recently (a year ago) had these questions and everyone gave very vague answeres so here's a really long post trying to be as detailed as possible, so that you hopefully experience less frustration than I did during that period of my life.
Here's my fairly recent (year-ish ago) experience with GRE.
For the physics GRE I found that I was not able to improve my score after preparation. I actually prepared for 2 months or more for the physics GRE with marginal improvement (woo a whole 10 points!). I regret wasting those two months, because I really spent a lot of time preparing, skipping out on social events and the like for 2 months straight. Luckily, my initial score was fairly decent, and a very high score was not a requirement for the programs I was applying to (they were in a different field, I only took this test because I had some 'making up' to do for some blemishes on my record), but still, there was definatly a lot of room for improvement, which did not come about after 2 months of rigorous preparation.
General GRE was a slightly different story. I found that my math score didn't need improvement (physics background > highschool math), but my verbal score needed a good 50+ points of improvement minimum (physics background < advanced vocab) to be competative for the schools I was looking at. I did the whole "word of the day" for a couple of months, and studied "common" word lists the week before the test. I took a practice test the night before the exam and it showed absolutely no improvement. But somehow my verbal score jumped a whole 70 points during the exam, so I'm not sure if that was a fluke.
All in all, this probably isn't good advice but it doesn't seem like preparing for either test helped me any, and the improvement on my verbal GRE was likely a fluke since it didn't show up the night before. If I had to do it all over again, given my results, I'd have just used my preparation time doing more productive things, like watching paint dry.
Dislaimer: Your results may vary
As far as how important GRE scores are, for me they were very important because the first 2 years of college I did absolutely nothing so GPA wise I was not as competative as other applicants. But I wouldn't say it was the most important. Things that were more important than the GRE for my application, in order of importance, are:
1. Letters of recommendation/research experiences. I got two amazing letters from professors I worked with, and a third letter that was only average (I'm guessing here by how much the professors liked my work and our discussions about recommending me.) I think the variety of research projects I worked on (5 different projects in a whole variety of fields) and the letters of recommendation that came from that were probably what got schools to let me interview with them.
2. Interviews. After getting my foot in the door from #1, I was able to use interviews to make good impressions. Key here is to ask questions about the research you are discussing with the interviewer. Try to ask specific questions but using a general vocabluary, so that you can let them interpret what is actually a stupid question as a good, relevant question. If you use terms that are too specific and ask questions that are crap they'll think you don't understand what they're talking about. If instead you ask questions that are specific but crap, but use a general vocabulary that is open to many interpretations to ask them, they will interpret the vocabluary on their own, and think you are asking a relevant question and have a good grasp of what you're discussing, even if you don't. Then you can nod and pretend that this is exactly what you meant to ask.
3. Doing really well in classes my junior and senior years.
This is really important in general, and was important to me especially to make up for previous shortcommings and prove to these schools that I wasn't entirely stupid, only somewhat stupid.
4. Personal essay explaining why I was a good fit for graduate work, for their program, and how my background would benefit their research etc. Also, make sure to BRIEFLY mention any shortcommings, but not make excuses for them. In my case, I had done less than stellar in my first 2 years of college, and I made sure to mention that. I said something along the lines, "Although my college career hasn't been without it's difficulties, as reflected in my first 2 years of college, I believe I have shown that I have the ability and drive to do graduate work, as reflected in my research experiences, GRE scores, and junior and senior years." Note that I mention the shortcomming, don't excuse it, and go on to say why they should still accept me even though I do have this shortcomming. This is something that was recommended to me by a professor in the admissions committee of my undergrad school, and it worked very well.
5. GRE scores. Basically, they are used in conjuction with GPA as an overall cutoff on whether or not the school will look at your application thoroughly. If you have low GPA you need a rather high GRE score. However, if you have a strong GPA, you don't need an overly good score to be considered. And if you are considered, 1-4 will be much more important. That's not to downplay the importance of GRE, but you will notice that schools have a range of GREs and GPAs they accept. If you are on the low end of their GPA range, you need to be on the high end of their GRE range, and vice versa. That should secure you an interview and thorough look at your application. After that, 1-4 are what will really matter.
As a sidenote, my background is someone with a low overall GPA (3.3) low freshman and sophemore GPA (2.5? ish in 1000 and 2000 level classes) and high junior and senior GPA (3.98 ish in 3000 and 4000 level classes), with a general GRE score in the low 1400s for Q and V (and a 6/6 on the Analytical Writing section), and a fairly large amount of research experience.
Now you might notice that most PhD programs have a supposed GPA cutoff of 3.5, which I lacked. However, even though I lack this I was able to secure a position in a very good and highly rated program in my field (comprable to the rankings of UCSD in biochemistry) and my top choice school (so it may be possible that I could have gotten in even higher using the mentioned methods if those schools appealed to me enough to apply) by compensating the shortcomming with other good things. And I also secured interviews from most of the schools I applied to as well, (most of which were highly rated programs), even though they all had GPA cutoffs much higher than mine.
Moral of the story is, GRE is important for acceptance, but a bad score can be made up for by other good things, as mentioned above.
Also, one final thing, let them know you're gay, or any other minority statuses. Seriously, I think this helped me get in too. I didn't say "Oh by the way, I'm gay", and I didn't even mention it in my essay, but I did put in my resume that I was a member of Pride Alliance (gay group) in my school in some schools, and not in others, and all the schools that knew I was gay accepted me, whereas some of the ones that didn't know, did not accept me (although a good number of those did as well, so it's not like it was the most important factor, but it did have significant impact I'm sure).
Hopefully this lets you know what you need to have a competative application, and I hope my story and experiences have helped you. GRE shouldn't cause you to despair if you have an otherwise strong application, but if you don't, then I suggest you invest more into a high score.