Quick review of generally how VPN's work: your computer, which is assigned an IP address by your ISP, connects to a remote VPN server, which has a different IP address assigned to it. The VPN server agrees to send and receive traffic for you, basically acting like a mail forwarder. Normally when you visit a website or check your mail the servers which you connect to will see your IP address as the originator of that traffic. When you're connected to the VPN server and you access a website or check your mail, those remote servers only see the IP address of the VPN server that you're connected through.
Now your question: since I'm connecting to the VPN's server at the same time as other folks, if they happen to do a Bad Thing and the FBI or other Three Letter Acronym Agencies get called in, will I be implicated since my traffic is also coming from this server?
The answer: very unlikely. The FBI/TLA's first line of investigation will be to identify and contact the owner of the IP address (ie: the VPN provider). If the VPN provider keeps logs of who was connecting to what (yikes), then they'll provide that to the FBI/TLA for correlation analysis. If the VPN provider does not keep logs, then that's up to them to fight that legal battle. While there may be public traces out there of you accessing other servers via the VPN (say, while logged in to a bulletin board which also logs your source IP address), that evidence is very circumstantial and is not likely to lead to any legal actionable investigations anytime soon. Legal investigation aside, any security analyst worth their salt that happens to be looking into an attack and traces it back to a VPN IP will assume that the attacker is using this VPN to mask their identity and will not conclude that every user of that VPN is also malicious.
tl;dr: Using a shared VPN is not likely to lead the police to your door anytime soon.