As an independent developer, I feel your pain. Here's a couple of things I've learned.
Time is money.
There's no such thing as "too small to bill". If I were to add up all the time I wasted doing small favors like this, I would lament for days about the amount of money I lost. It adds up, and the more you give the more they will take.
This is human nature. If every day you ask someone for $10 and they happily hand it to you and assure you that it's no problem, you're going to at least be tempted to ask tomorrow. Now since it's not actual money being requested, you're going to feel even more inclined to ask for it because after all, it's just time right?
Maybe you don't always bill for a full hour, but bill something. You must.
Also remember that, especially when you're a skilled laborer, nothing takes "only 10 minutes." It took you years and, if private education was involved, probably thousands of dollars to be able to do that thing in 10 minutes. By forgetting this, you devalue yourself and your craft.
It's going to ruin your relationship with your client, not help.
Eventually you're going to begrudge your client. This is understandable, because an unnatural relationship has developed. You've allowed what should have been a symbiotic relationship to turn into a parasitic one. Nobody likes ticks.
Plus, eventually you're going to say "enough" and you're going to start doing what you should have done in the first place, respond to every inquiry with a quote and an estimated time of delivery. Your client, who now views themselves as some sort of buddy of yours is probably not going to take this well. They've been allowed to believe for some time that you don't have a business relationship (because it hasn't been one), but that you have some warped version of friendship where you do nice things for them because you're their buddy.
Imagine turning to your best mate one Friday night when he asks to hitch a ride to the club and handing him an quote for the drive and your time as a response. That's crazy and bass ackwards to imagine, because that's what it would be. You're suddenly imposing the rules of a completely different kind of relationship, one that you don't have together.
If you need to do freebies to get or keep a client, that's the kind of client you don't want at all.
Often in small business, we have this inclination that if we just do favours for a client, we'll do well. This leads to under-quoting jobs, completely throwing away your time (which remember is the same as throwing money out of your pocket) and such. Doing business this way, you will fail in the end and these clients will live on. If you feel like billing fair market value for something might make your client leave you, do it anyway and use their parting payment to buy a bottle of champagne and celebrate because you've just been saved from operating at a loss.
I can tell you that every single client I've done more than one freebie for no longer does business with me. Every single one. The clients I maintain and have an amazing business relationship with are the ones that understand that when they ask me do something, they'll also be asking how much money to send me.
Freebies aren't always bad.
There are cases when doing a freebie can be a pure positive. Showing appreciation to a loyal customer, helping someone in need, etc. I'm not necessarily saying that all freebies are bad, but rather my answer is given in the context of the question: a business relationship turned sour by undeserved or unsolicited freebies.
My answer is addressing the very poor business practice of giving away things for free arbitrarily for the sake of gaining or maintaining new clients. The resulting situation, as described in the question usually isn't the clients fault, but is self induced by the person who suffers: the person giving away their goods or services.
For those who want to know how to fix the current bad relationships
Look, so far I've written this long answer and I was happy to do that, but I've got a lot of other priorities I have to take care of and I can't keep doing this for free. I've got to eat. My hourly rate is...
That doesn't go over very well does it? Once you've established a certain type of relationship with another person it's nearly impossible to try to suddenly switch it to a completely different type of relationship or interaction. I've had "the talk" in every way possible and while it might go over smoothly in certain ways, inevitably that client disappears from the "recent calls" list on your phone.