I have a fairly technical Twitter stream. If I was to use a resume to apply for things (I don't) I would be sure to include it. If I forgot for some reason, and someone asked for it, I would provide it without hesitation, along with a rough estimate of my followers etc.
But if your Twitter is non technical, full of pictures of beer, dirty jokes, swearing, strong political opinions, and nothing that would make an employer think "I want this person on my team!" then keep it to yourself and your friends. On a form, leave it blank. If they ask, just say "I don't have a technical Twitter." Similarly for Facebook. If you routinely share links to technical material, reviews of conferences you've attended and books you've read, and you don't share pictures of yourself getting drunk or the like, then you could include it, if not say "Facebook is only for close personal friends." Your LinkedIn of course should be entirely professional, that's the point of it. You might also consider your StackExchange activities to be entirely professional too, and might operate here under a handle rather than your real name, so providing your handle might be a good idea, or a link to your Careers profile.
If you tell an interviewer, "I don't have a technical blog/Twitter/Facebook" they might push you to reveal it. But a form you're filling out to get an interview will not. So reveal only the profiles that make you look good technically.
I believe in an interview it would take tremendous chutzpah for an interviewer to tell me "oh that's fine, I don't want to check your technical profile, I want to look you over personally." If they did, I think I would just go with the firm stare that lasts long enough to let them know they've done something they shouldn't, and then repeat "I don't have a technical Twitter" or whatever and sit quietly. It's hard for me to be sure, because the only Twitter I have is technical, the only blog I have is technical, and I have a "public figure" Facebook. But I have been asked overly prying questions before and I find that it works: just stare for a little too long and then either repeat your previous non-answer, or say something meta like "if you're trying to find out more about my internet presence, " and then provide a roughly equivalent piece of information. Back in the day women would be asked about plans for marriage and babies, and I would do the stare and then say "if you're curious about my long term career plans I'd be delighted to discuss that" and go on to say what I wanted to do (at work) over the next 5-10 years. You could take a similar approach to overly prying requests for internet profiles.
And if you don't have any technical profile at all anywhere, consider getting one. It's free and easy and makes you look much more valuable.