Is it safe to eat genetically modified foods?

Genetically modified organisms (GMOs) are plants, animals, and other creatures that have been modified through genetic manipulation to make them better to eat, easier to grow, faster to grow, or other combinations of beneficial traits.  This can be anything from pest-resistant corn to fast-growing salmon to vitamin A-rich rice. For some reason Europeans get very bent out of shape about GMOs, but Americans worry less about GMOs then they do about organics, etc.  Still, there are some falsehoods that fly around out there.
Humans have been "genetically modifying" animals and crops for thousands of years, ever since we switched from hunter-gathering to farming and animal husbandry.  We select for genetically advantageous traits whenever we breed the fastest racehorses together, or the fastest growing soybean varieties, or cross two type of apples to make a new, delicious type. 
The difference is now, we can do it in the lab faster than through selective breeding, and we can put genes from one species into another species.  "Genes" are the units of our DNA that tell our cells what to do, what to make, and they define who and what we are.  Some people worry that GMOs that are produced in a lab are somehow "different" from natural varieties, and dangerous.  Well, they are different in whatever trait they have been designed to have, however, eating GMOs will not specifically do anything to us.  You see, it is hard to swap genes around and make these modifications.  Once the gene is inside that organism's genome, it is there for good.  It's not coming out again, it's not going to pop into you somehow and make you a big salmon or something.  I have genetically modified breast cancer cell lines myself in the lab, and it's hard work!  You have to start with a billion-plus cells, then use a specially-made virus to get a gene into the cells, and then sort out the 0.1-1% of cells that actually incorporated your special gene.  And that's under ideal conditions and trying to do it!     
Think about it this way:  When you eat a bunch of green spinach, you're eating spinach DNA.  Yep, you are.  You don't absorb the spinach DNA and start making chlorophyll, and you don't turn green, do you?  When you eat chicken, you don't absorb chicken DNA and start growing feathers!  The same is true for GMOs.  Their genes are fixed, they're not going anywhere and they won't do anything weird to you.  There is one group doing really great work, producing vitamin-A-rich rice to eliminate severe life-threatening vitamin-A deficiencies in the developing world.  Some people that fear GMOs try to block them, but I hope they get educated enough to stand aside and let this group save lives.  http://www.goldenrice.org/ 
However, GMOs are truly safe to eat, but they are not harmless.  Think about the fast-growing big salmon. They would be just fine in a fish farm tank, getting big and delicious.  However, if some idiot were to throw them into the ocean with wild salmon, the modified salmon would out-compete the native fish, eat all the food, and takeover.  I believe GMOs should be carefully monitored and grown under controlled conditions, and traits that would give the modified organism a huge natural advantage over its native species shouldn't be allowed. But vitamin-A rice, I'm all for it.  Why not save a few lives with science?