First question though, is there anyone nearby who would do that, eg shared household, work colleagues, (if at work), etc? If not, that removes one source of risk.
I assume this is Windows. If so, is your login account password protected? If this is a different account to the original System Administrator account that came with the computer, is that account also password protected?
When the system wakes up, where does it wake up to, the Welcome Screen? If so, and if all accounts are password protected, then that is reasonably safe. If it wakes up into your own account, eg the desktop, then anyone can continue using it.
Do you have a firewall installed? If so that will help prevent all but the serious hackers, (and serious hackers generally don't bother with us minnows).
Is the system connected to the internet wirelessly? If so, which wireless security are you using? WEP is not good enough and you need WP2A and with SSID turned on with a strong password. Those make it extremely hard for wireless hackers to gain access.
I turn my laptop on every morning (connected to power and with battery installed) and wnen I want to leave it for half an hour or more I put it into sleep mode. I find this is much quicker coming to life as hibernation takes as long as rebooting. I do this throughout the day. I turn it off if I am going out for several hours.
I have now been told this is dangerous and that someone with malicious intent could invade my setup because this is easier to do when in sleep mode.
Is there a real expert out there who can advise?