There are a few factors here - the biggest being how actively is the 'competitor' trying to access your data?
Real World - 99% of the time, people aren't going to try and hack into your computer and possibly won't even be monitoring what you are doing. That doesn't mean you shouldn't take common sense precautions or rightfully ask about what's possible as you have done so. All I'm saying is these measures will only be needed in the minority of cases.
The other 1% of the time, they may be monitoring your traffic trying to see what you are doing, or casually probing your computer. This means they can view any information you send over any site that begins with http (logins, etc), ftp, see what sites you're visiting, etc. In other words treat anything that begins with http as insecure and assume they can see it. If it begins with https you're typically (within reason) safe, as this encrypts the information from your computer to the sever, so any information you send (emails etc) they can monitor - but they will only get scrambled garbage. Another thing to be careful of is poorly configured file sharing, it may be the case you've set up the ability for others to look at the files on your computer and possibly read / write to it. Be careful of this.
The 0.001% of the time, I'm talking you work for the US DoD and you're having a conference in China, you may be subjected to direct attacks. In this case pretty much all bets are off and depending on what you have running you could be completely safe - or they could gain complete control of your computer.
So given these levels, what can you do?
- Assume nothing sent over http is safe, chances are it is, but assume it's not.
- Use a VPN, this encrypts all information leaving your computer to an external server. Think of it as https for everything.
- If you're getting into 0.001% territory, and you have something that's actually valuable on your computer the best option is just to not plug it in. Get a mobile modem or use some other method. Much less convenient, much more safe.
As with all security, there is no right answer. There is simply convenience on one side and security on the other. You have to slide along the scale to suit your needs.