I get this uncomfortableness! I used to worry about this too. And I got a lot of funny looks, when I thought I was being polite. Here's how I figured it out:
It helps when you realize that English is the weird language. Many romance languages distinguish between formal and informal using a tense (usted v tú). But in English, we make things sound polite by adding more conditionals to a sentence.
"Bring me a coffee" v "Would you mind terribly, if you are not too busy, possibly thinking about maybe bringing me a coffee, if it's not too much trouble, thank you very much please?"
Obviously this is an exaggeration! But you get the idea. In English we add politeness by making our sentences less direct.
In English, "I would" means a lot of different things, grammatically. E.g., it means "used to". As in "Every morning I would drink coffee before school"). However, it also signals that you are being polite in a request. "Would you mind getting me a coffee?".
But "polite" doesn't translate into Spanish, so you are just left with the other grammatical meanings.
When you say "I would like a coffee", you are essentially doing a literal translation from English. Which isn't correct!
If it's hard to get over the idea that you are being rude, if you don't use "would", then imagine that when you say "me gustaría un cafe", what people here is "I used to like a coffee." They get what you are saying... kinda... but it's weird.
As people above suggested, convey politeness through your tone and using please/thank you. After all, tone is really the most important thing in any language... as we know in British English from the sheer venom that can be injected into "terribly sorry".