Must Egypt be done on tour? Safe to travel on own intinerary with taxi from train station to attractions?

Not safe for Americans, especially if you are a female.
http://travel.state.gov/travel/cis_pa_tw/cis/cis_1108.html

I have travelled to Egypt and the people are very friendly and hospitable. I would go there again in a heartbeat if I had more money. Personally I do not like "tours" but in Egypt it's not a bad idea. We actually did a Nile River cruise which offers you a little more flexibility with what you see, but provides regular accommodations, meals, etc on board. I highly recommend that. If you still prefer to go on your own, I would suggest doing a lot of research online first to make sure there are connections in all of the locations you plan to visit so you don't get stuck anywhere. Also, things can be a little unpredictable there. For example, while we were there a major sandstorm hit by the Aswan Dam and Cairo lost electricity for hours. It was insane! Also, I DO NOT suggest renting a car. They drive crazy there - the craziest I've seen anywhere in the world so far.

Generally speaking Egypt is safer than a lot of countries,therefore, it is possible to make your own itinerary but you must do some reading on the net or the lonely planet guide on Egypt. If you are a female it is not advisable to travel on your own.
Taking a tour will be more expensive but you are saved the hastle of where to go,language problems etc.

I travelled to Egypt earlier this year. I had 1 day before and 3 days after my tour to deal with myself.
I am Australian and female and I found I had no problem getting around by myself during those days. The hotel staff were more than happy to help me with directions to the museum (I walked to and from my hotel), as well as organising taxis to get me to other places.
Having said that, the time I was on my tour was definitely worth it, as the tour guide has all the hassles of getting tickets and organising transport and they know the local language most of the time - I went with a tour company called Geckos and our Egyptian tour guide was awesome.
On tour they also take care of all the tipping and "Baksheesh" as it is called in Egypt is very common and people will ask for it for simply saying hello to you at a temple, so you need to beware of that.
Definitely do lots of research, as someone else said and maybe do a mixture as I did. It's a fantastic country, particularly if you have had a fascination with it for years like I did.

it is perfectly safe to go with a taxi.
however, when you go with a tour, you will have a guide who points out imp things to you. you will see places of importance . better go with a tour.

Yes it is perfectly safe. If you are planning to do it yourself get a copy of the Lonely Planet Guide to Egypt and quite honestly it is as good as having a lot of guides you would pay 100LE plus for.
I worked as a tour guide in Egypt while I was studying and found this book an incredible help many times.
Now I live in Luxor but I still carry my copy of The Lonely Planet Guide to Egypt in my bag or the glove box of my car everywhere I go!
I suggest you make your hotel booking before you leave for Egypt as it is much cheaper that way.The recommendations given in The Lonely Planet Guide are made by secret travellers, no business can pay to get their service or business into its recommendations. These come in Budget, Medium,and Luxury levels of hotels and restaurants.
From the moment you get of the plane you will be able to follow your L.P.Guide as it gives you advise on everything imaginable, including how much to pay for taxis, how to bargain,how much to pay for 'baksheesh etc. etc.
Feel safe, you will have no problems and have the holiday of your lifetime which ever way you choose to come.
If you do choose to come with a tour, use a tour company that has representatives in your home country don't rely on fancy websites as they can be very misleading.
If you need any further information or tips email me.

It is safe to do it alone, BUT reservations in hotels are difficult without the help of an agency. Hotels are fully booked most of the time. With the heavy traffic in Egypt you may not be able to estimate how long it takes to reach any destination. Trains and planes are full most of the time. Travel agencies book in advance, they know that they can fill the reserved places. Taxis at rush hours are hard to find. Guides will show you the most interesting monuments and will point to the interesting details. If you do not arrive with a group, most of the time you will be by yourself with the guide, thus your interests and preferences are met. To make it short, if you do it by yourself it will need a longer stay. With a guide you can see much in one day.
It can be done alone if it is your second time, but for a first timer I strongly advise you to book with and agency.