I have spent the last two days looking for just such a tool although mine would have to support the insertion of images. I have downloaded four, which all looked good initially but I found performance problems in all of them.
There must be a lucrative market waiting on the first people who produce a decent, robust, web based editor that designers could build into their client's sites.
Have a look at the FCKeditor. It has a load of options and can do anything you want it to, including uploading and inserting images. Integration with a server-side app is very well possible; both PHP and ASP are supported.
Downside is that it is a rather resource-intensive tool.
Downside of all rich text editors I've seen is that in IE they tend to deliver rather crappy code. Uppercase tags, and such things. Don't blaim the editors, it's some Windows component that is responsible.
I have used FCKeditor on four or five occasions. It does the job but it stopped working on one of the sites I had installed it and I got it in the neck from the site owner. When I took it up with FCKeditor support they tried to fix it but failed, blaming the hosting account.
After buying an unlimited install licence I have had to buy another editor, EasySiteEdit, which I must say looks excellent. They even install it for you and support so far has been great. The only downside is that users cannot access the HTML to make changes to the META content but this is to be included in the next release which is due very soon.
I am currently using EditPlus2. I have found it extremely easy to use and it supports a lot of functions. It is free to download and it is very inexpensive if you decide to purchase it after 30 days. At least you can try it for 30 days to see if it performs as you need it to.