Is it possible for someone to unlock your front door get into your house and then lock the door again without being supplied with a key?
Yes, locks can be picked, or bump keys can be used. There's no difference in using these tools to unlock vs re-lock a lock.
There is no such thing as perfect security. If there was, it would have infinite cost.
What you want is security that is Good Enough. For most folks, that can be defined as "just a bit better than your neighbors, so the burglar bothers them instead." Remember that the burglar generally isn't targeting you in particular; they want to minimize risk of being seen and caught, and they're not going to spend more time visibly trying to break in than they absolutely must.
So: A good (not necessarily great) lock, reasonably (not necessarily perfectly) resistant to common modes of attack, mounted well on a strong door in a strong frame (kick-in is more of a real-world risk than picking). Deadbolt with a 1" throw, again well mounted. Door that is very visible from the street, and ideally well-lit, so anyone playing with it will feel exposed.
Also consider the security of your back door, basement door, and windows. Basically, any way that your teenage kid might try to sneak in or out after curfew is a way that a burglar might try to sneak in. Make sure hedges are trimmed back, don't leave ladders outside and unsecured, et cetera.
Next step after that would be alarms. For most people, in most cases, I'm convinced an alarm is more trouble than it's worth; the police now require that alarms be silent with contracted monitoring services in many cities and suburbs because false alarms were unacceptably common.
For most folks, burglar-resistant window grills come after alarms these days, simply because they're ugly... and because they can block escape in case of fire. But they do have their uses.
AFTER considering all of that I'd consider going to highly pick-resistant cylinders... unless your situation has special requirements you haven't told us about. Seriously, most folks who have the patience to learn to pick locks well enough that they might be a danger to you also have the patience to hold down a real job, which will pay a lot better for a lot less risk!
Re Debbie's question, "So someone can break into your home without there being any evidence of a break-in?" ... Maybe. It depends on what you mean by "evidence". In theory, lockpicks leave marks inside locks which an expert can distinguish from those left by normal use of a key. But that certainly isn't something you're going to notice as a homeowner, and not everyone considers "forensic locksmithing" a reliable process. Certainly your insurance company is likely to resist paying unless you can point to some stronger evidence of "forced entry". That gets back to the "good enough" clause; from an insurance point of view you'd actually prefer that they kick the door in or break a window.... or set off an alarm. But selective additional protection of valuables may be a better answer than protecting the whole house. And, again, this is presuming an unusually skilled intruder; most are shake-the-knob smash-and-grab types.
Finally, remember that (a) the best security in the world does no good if you don't use it, and (b) if you think someone is getting into your place on a recurring basis, it is FAR more likely that you're fooling yourself into believing this... even if it's more comfortable to think someone else is taking things or moving them around than to believe you're starting to suffer a bit of forgetfulness.
Door locks are just a deterrent. If someone wants into your house they will find a way. A bump key is one way, but when they bump your lock, it ruins the cylinder. So they're not opening it the nice way with a spare. They're bumping the pins so they don't need the original keys. Good luck! Maybe try re-keying your locks.