I definitely feel this way about my job, lol.
When I was younger, my family discovered the Enneagram personality test and we all took it. I remember being annoyed because my personality, no matter how many times I took the test, came out as a 2 (The Helper). It's actually a pretty interesting personality test, and I wouldn't be surprised if a lot of submissives results were also a 2.
I tend to fight my nature a lot, though. While I have a desire to please and take care of people, and whenever my friends have problems, a lot of them have told me I'm the first person they call, I'm picky about who I choose to trust and be that way around.
People will take advantage of your trusting and submissive nature. As others have said, some people will try to get what they want regardless of what it does to someone else. If you can recognize when it happens, when someone is using you, then you'll have more power to stop it. Be pickier about who you trust and who you surround yourself with. Friends, even knowing of your behavior, shouldn't seek to take advantage of it and when they do, you should call them on it.
One of my friends back in high school ended up using me as basically a taxi service for her and her boyfriend. I also had a very hard time saying no, but once I reached my limit and was pushed too far, I let her have it. I basically cut her off and told her that I couldn't be friends with someone who would abuse my trust without any regard to how it made me feel. A week later I got an apology letter and a CD she'd burned specifically for me saying she was sorry she'd been such a poor friend. We're still friends, now nearly a decade later, because she recognized that there were limits and I learned to say no more often.
It's hard to say no, especially to people you care about, but it's necessary to making sure you don't feel used. True friends would never want to make you feel this way.