I don't really approve of taking advantage of school security. It's a school (and from the sounds of things, a high school/juinor high), not a bank or something, so I wouldn't expect them to have particularly strong security.
That said, I did tend to explore what I 'could' do throughout the years.
Elementary school: I don't think we had internet, and so I don't think the computers were even networked. I knew how to use DOS, so I was the 'computer guru' that the teachers turned to, and basicly I could do whatever. The library computers were slightly better and were password protected in order to login and was perpetually supposed to stay within some book searching program. I ended up restarting one and discovering the password was needed, and the librian just told me the password, so yeah, no security in elementary land. Not that it was needed.
Junior high: I volunteered to help the tech guy with 'tech stuff', which mainly consisted of reinstalling windows a lot. The computers had Deepfreeze on them which always had to be disabled prior, so I eventually was just given the password. Later on, he ended up letting me use his account, which basicly equated to giving me admin powers in novell. Largely useless to my non-disruptive self. I did give myself infinite print credits, but I never printed much anyway so it didn't matter. Also of interest was that his password to his computer account was the same as to his admin account for our webmail service, which happened to display some students passwords uncensored. If I'd been so inclined, that could've been valuable information given so many people use the same password for everything. (Although 'school' was a pretty common password too.) Towards the end of my juinor high stay the school board technician visited, and he 'may' have left a binder containing the school-board account and password in it. It was left in the school's tech guy's room where students normally wouldn't be, and I'm sure the school board wouldn't have approved of the trust I'd been given, and so the school board never knew. Also, I could send messages to anyone, which wasn't normally allowed.
It never occured to me to explore teacher accounts for tests and the like, but I was getting 100's normally anyway. If any of the teachers did store tests and the like on their accounts though, I probably had access. Although, I have strong reason to believe that if I'd known how, I could have editted all of my final grades anyway.
High school: There was a computer acceptable use policy thing, I never got around to signing it. Some half page thing basicly in any case. For the most part much better security. Most sites were blocked, and more were blocked regularly, and they could apparently remotely monitor and close windows/send messages if someone was caught bypassing it. They wern't terribly vigilante though, so proxy avoidence usually worked, I only had my stuff closed down once. I eventually managed to guess the substitute teacher account password (schools mascot I believe), which had some limited access to stuff student's shouldn't have. This might have been useful, if I still didn't have access to the aforementioned school board technician account, which had access to everything. Most teachers made their tests/exams at home and/or kept them on a memory stick rather than their school accounts, but old editions that they were modifying into the ones they used were usually there, which may have given me a bit of advance warning on what sort of stuff I needed to know. I could see every student's grades too, which satisfied my curiosity about various people who tended to be tight lipped about their marks. I never let on I knew though, so I'm justifiying the invasion of privacy there with 'what they don't know can't hurt them'.
I could also remotely restart computers (run... cmd worked, and they didn't restrict much there), which was fun to play with. I'd always log myself on to the target computer first (by physically going to it and logging in) so as to be sure that I wouldn't disrupt anyones work, but the fact I 'could' amused me. This I ended up showing a couple other people (not how to do it, but that I could), and that probably wasn't wise. Apparently a couple other people figured out how to do it anyway, and some people ended up losing their computer account and were suspended for awhile. I wasn't linked to it.
You could also login as guest or student and such and browse anoymously, however this they did catch very regularly, so I didn't do it myself (as I could basicly be anonymous through the use of the various other accounts I had access to). Saw lots do it though.
In my last year, a vice principal approached me saying the tech guy had emailed her with a 'long list' of things I'd done wrong, and a recommendation that I be suspended for a very long time. I'm dissappointed that I never got to see that list, as I was quite careful about having things not linked to me (I don't think I ever did anything wrong on my proper student account, except perhaps proxy use, and even then a reasonable amount of the time it was so I could access forums that were actually academicly related to some degree (physicsforums, here, etc.). Anyway, since I had a 'good history' and similar such things, the vice principal (who incidently wasn't particularly computer literate) apparently chose to actually argue for a lesser punishment, and I ended up losing access to my student account for a couple weeks, and that's it. Incidently, that worked out great for giving me an excuse to not be able to work on a couple computer based in-class assignments, so I got to hang out with a couple friends as they did theirs. The school board tech account pass wasn't changed either (presumably meaning they didn't realise anyone had access to it, so I wasn't caught on that), so I just used it for my spare time computer usage so I basicly got away free.
University: No obvious holes, not willing to poke at it for holes. I'm paying money to go here, and they could quite easily just kick me out for messing with stuff, so trying seems stupid, no matter how sure I may be that I won't get caught.
They're not too restrictive though (no 'offensive' material in a publicly viewable area [which I notice doesn't forbid it outright, so I could in theory browse porn on my university account and not be doing anything wrong
], and don't pirate music [or anything else], as they can and will track you down) and as I'm not typical the piratey sort, nor do I have any strong desire to view any offensive material at school, it works out.
The most tempting thing is probably to get maple off the university computers, but depending on how loosely they determine "staff" I might be able to get it legitly from them anyway.
So, that's my longer than expected story of my history with school computer security.