Occasionally it's even a relief. Have you ever made plans with somebody, realised the day of that you don't really want to, and then receive a text message saying THEY can't make it?
You get out scot-free and play the "don't worry about it, next time!" card, when secretly you're brimming with relief inside at the fact you won't have to put on a full face and talk to another human for the night.
Yet if you're going to cancel plans (or say no upon initial invite) there are good ways to do it and bad ways to do it. The biggest faux pas? Knowing you are going to cancel for days, but leaving it until hours before you're due to meet somebody. I have no idea why people do this. If you're going to cancel, give people a good 12 hours (at least) to replan their time.
The most efficient (and courteous) way to cancel plans is with pure honesty. Not the white-lies version that lets you maintain your decorum – e.g. saying you double-booked, you have to work, or you're "not feeling well".
The real, warts-and-all version: you can't afford it, you look like crap and you need some sleep, you can't shake off the Black Dog, or you have diarrhoea. Seriously, people appreciate the cold, hard truth.
The concern exists that somebody will begrudge you for cancelling. They'll think you're rude or lazy. Worse still, they'll think you're cancelling because you don't want to see them; as if it's personal. This is why the complete honesty approach works.
Your excuse for being unable to make it is about you and your personal issues, not anyone else. In exposing your raw self (via the real reason you don't want to leave the house), I think you come out looking better, not worse. Nobody puts a black mark against you for revealing your vulnerabilities.
Something I really struggle with is making social commitments weeks in advance. You know the situation: you're asked if you're free three weeks from Saturday, so of course you say yes.
You commit to something like a BYO or a child's birthday party or a 5-hour hike. But as the day nears and you have a more realistic idea of how busy/tired/overwhelmed you are, you scream to yourself, "Why did I commit to this?" It sounded like a fine idea at the time, but now you really, really don't want to go.
In these situations, one of two options are normally applied to cancelling. Either you're vague upon initial commitment (phrases such as "will pencil it in" and "will try to make it" are oft used here). Or, you can commit, but then never follow up, so when the week arrives (pending no contact from either side) you can presume the event is not happening.
Neither option is really all that honourable. That's why I've been trying this tactic: I say to people, "can I let you know the day before?". If they say they need more notice, that's fine; I just decline. For me, it does away with the stress of being committed – I know I have "an out".
Some probably consider me a bit of flake now, but I'm okay with that. They've all cancelled on me enough times themselves for me not to care.