In homosexual relationships, is there really always a dominant partner and a submissive one? Or is that just a stereotype?

I wouldn't say this is the case at all, any more than it would be the case in a heterosexual relationship. Both men (or both women) see and treat each other as equals, and they often switch roles during sex.

There will always be social situations where one partner is more skilled and/or popular than the other, and that happens in all relationships. But in the end, it's all about trust and respect, and you can't have that if one partner is always dominant.

I make the same argument for heterosexual couples. Often, the "submissive" partner feels confined or controlled when the dominant partner is always making all of the decisions and basically trying to control the relationship. Or, if a partner always wants to be submissive, the "dominant" partner may feel neglected, worn out frustrated with the fact that s/he always has to be the "bad guy." Additionally, the dominant partner in a relationship isn't always the man. A good example of this in pop culture might be Tom and Lynette Scavo from Desperate Housewives. Her personality is clearly more domineering than his laid-back world-view.

It's one of the reasons I don't like the fact that the Edward/Bella relationship in Twilight is depicted as healthy, when Bella clearly isn't treated as an equal by Edward, but as something he needs to protect. But that's a digression. :o)

Didn't you just ask this on the random club this morning?

Each relationship, whether gay or straight is all about the equal rights between the partners. Unless you're into the slave/master theme, then each partner has a responsibility to be the dominant and the reciever at some point during the relationship.
It all depends on what you and your partner want out of the relationship and which role you so wish to play a part in.
Most relationships aren't like this, they're just equal to each other.
Although in my experience, more of my female gay friends seem to have the dominant/submissive type, while my male gay friends are both submissive and equal to each other. So i guess it all depends on your personality and what you hope to achieve out of the relationship yourself.

There is a fairly large segment that meets that demographic. I understand why you may want to stereotype gay couples as that combination. That is but one segment, some couples are both versatile and egalitarian. In rare cases you find the more effeminate one makes the decision and the masculine partner just sits back and goes with it. You probably notice these same dynamics exist in hetero relationships. There are more similarities than differences between couple gay or str8. I gave just 3 examples.