There are a few companies I've interviewed with that I'd have loved to work for, but they've passed over me for "not enough experience". I really want to re-apply to the same positions but I'm wondering if it'd be unprofessional to do so after just 6 months or so. How long should I wait before re-applying?
There's no real set "rule" for this - if you've been passed over by a company for a given reason then there's no point in re-applying until the reason no longer applies.
If they have passed you over for "not enough experience" then that can be a little nebulous. If it's "not enough general experience" then you are unlikely to be able to significantly change that in 6 months. 6 months isn't a long time really.
On the other hand if it's "not enough experience in specific technology x" and you've spent the last 6 months living and breathing technology x for 40 hours a week then it might.
It's always better to err on the side of caution here - reapplying too soon/too frequently is one way to irritate the heck out of a hiring manager. Ideally try and get the objective advice of a third party you trust to see if they think you are really showing a substantial change in experience but failing that I'd say if you're questioning yourself whether it's a big change in experience then it probably isn't.
In general, no one can tell, as this is based on the company recruiting guidelines. And sometimes people change and the guidelines with them.
Best is to ask whether it makes sense to reapply and when! Most companies will happily tell you their current guidelines. If you are very lucky they might also give you personal feedback as to how much sense it makes to re-apply based on how well you did in the interview.
That being said, some rough guidelines:
For the same positions: wait at least 6 months, better a year. If they specify a minimum experience level, wait till you reached it (or at least are very close).
For positions at a lower level: Apply anytime. Unless their dismissal was in general for any position at their company.
For positions at a higher level: Wait at least a year. If they specify a minimum experience level, wait till you reached it (or at least nearly).
For positions at a different domain: Apply anytime. Unless their dismissal was in general for any position at their company. If they specify a required number of years of experience, wait until you at least got half of them, if you haven't yet.
Reach out to a recruiter and ask when they suggest you apply. A recruiter for the position you're interested in will be able to best advise you considering your total experience. Companies will frequently relax experience requirements if you demonstrate capabilities another way - a recruiter can help you find ways to do just that.
Keeping in touch with recruiters are companies you're interested in has a number of additional benefits:
1. You're the first person a recruiter will reach out to if they have a new posting. If a recruiter can fill a role from existing contacts, they will. Posting on job sites adds work they would rather avoid.
2. Your profile will be familiar when you do apply again. Occasionally calling and chatting means a recruiter will recognize your name - a good thing for getting past early resume screening.
3. Your profile may be forwarded to other recruiters. If another company is trying to fill a role that better matches your profile, a recruiter may put you in touch with the other company -- good will between companies goes a long way.
Good luck with the job hunt!
The amount of time you should wait would depend on what reason you were given for not getting the job. For your case specifically, where you were told it was because of "not enough experience", then I would wait at least a year, probably more. The main question you need to consider is whether the amount of experience you have gained during your time working is enough to change their opinion of you. If they said you were specifically lacking experience in X and you've been working on a project where you've used X every day for the past 6 months, then you might be okay. If they just generally said you need more experience, then they want you to have more time working in your field in general and you may need more time.
Now if they gave a different reason for rejecting you, or if you were applying to a different position, then that would change the answer entirely. If they liked you but someone else was better, then feel free to re-apply to any new open positions without waiting at all. If they said they didn't feel you were a "good fit" for the company, then I would give up on that company, or at least that group within the company.