I'd like to supplement eliserh's excellent write-up on this subject, over at hormone replacement therapy, if I may.
Since I started taking oestrogen a few years ago, I've noticed some changes in my mind, and probably missed a bunch more besides. For what it's worth, here are ways in which I think differently to how I used to, that I speculate might be caused by this hormone.
Noticing aesthetic beauty in things
I distinctly remember when I was many years younger and my mother bought a yellow CD player just because it was yellow and would therefore look good in the kitchen next to a lot of other yellow appliances. At the time, I couldn't believe she would rather buy something for how it looked rather than how well it functioned at its task (in this case, playing CDs in a non-tinny way, at which it failed miserably).
Recently, though, I've been looking at a certain modular synthesizer over others, mainly because it's an all-in-one unit with a built-in keyboard, in a beautiful wooden case. I've also been looking at Mac OS X, despite my political inclination towards free software, because it looks like it has the most slick GUI I've ever seen. I'm sure that, to some extent, my values have changed in terms of why I desire certain products over others. Now I care about aesthetics as well as functionality.
Empathising with fictional characters
Although I occasionally watched romantic films before, it was nothing compared to the experience it is now. I finally understand why they're so popular: even when I'm watching a kid's film, or a badly written film, even while I'm actually thinking about how badly written it is, I can't help but cry involuntarily when the two good characters get back together at the end, reunited at last. This still applies even if I've seen the film many times before. I even cried when Data talked about how he missed Geordi in Star Trek, when he thought he was dead. If an episode of Star Trek can make someone cry, imagine what a well-written, emotionally charged romantic film can do for that person.
Empathising with living creatures
Shortly after I started taking oestrogen, I became a vegetarian, a few years later going all the way and becoming a vegan. While this seems rare amongst the transwomen I know, it's worth noting that there appear to be more vegetarian women than vegetarian men1. (Of course, it's possible that the reason I wasn't a vegetarian before was simply that I was too depressed to think about such things).
Never being alone thanks to stuffed toys
When I was a teenager, I dismissed stuffed toys as being for kids. Since then, my partner and I have immersed ourselves in countless stuffed toy animals. We hug them all the time, we sleep hugging them, and sometimes I can even see how they're lonely when they're in a room all by themselves, but happier after I hug them, just from their inanimate facial expressions.
In short, if you're a transwoman about to take this hormone, the benefits of finally being able to think like you always should have done can be every bit as good as growing breasts and developing attractive curves.
Of course, it'll probably help that you won't be constantly depressed any more, but that's just as true of transmen taking testosterone. It's not specific to any particular hormone, just the wonderful effect of taking the right hormone for your own particular mind.
These are just my personal experiences. It's impossible to tell which changes were caused by oestrogen, which were caused by not being depressed since admitting to myself who I was and changing my body to more accurately reflect that, and which were simply caused by me growing up.
1. http://www.vegsoc.org/info/statveg.html - Out of a poll of 1051 university and college students conducted in 2002, 11% of women claimed to be vegetarian, whereas only 4% of men claimed to be such.