Well I have done this in the past for my PhD and although I ended up with two offers it wasn´t a good experience. Mainly because I felt really guilty towards the people I had to turn down in the end although in the beginning i really sounded anthousiastic and so on about their work. So I decided not to do the same for my postdoc applications ending up with 5 rejections so far to positions I applied one after the other. Now seeing the day my contracts ends approaching I feel like applying for as many jobs as I can find. Although I know this should be ok knowing that our specific scientific community is very small it still feels akward doing so. People all know each other and contacting a potential supervisor personally already feels like a commitment to me. Somehow I feel contacting many people personally and expressing interesting sounds kind of dishonest.. or is it just me being stupid? In addition what happens if a person says ok come but you wait for an answer from a person offering a ´better´ position? I´ve been there before and I just told the first person. But still it felt pretty bad. what would you do and how do you handle such a situation? I am afraid in the end ending up unemployed I will regret missing out on chances just because I didn´t try them. What do you think? (sorry for my long post.)

There is nothing dishonest about being genuinely interested in more than one thing at once.

The vast majority of people would be understanding about a person making multiple applications simultaneously. There is nothing to feel guilty about unless you're proposing to do something sneaky in playing people off against each other or going after jobs that you would never ever accept, but it doesn't sound like you would. So if there are multiple jobs out there that are suitable for you and interest you to some extent, apply to them all. It may lead to an awkward situation if offered more than one job, but that's better than being offered no jobs, and besides there are ways you can handle those kind of scenarios without causing big dramas for the people offering the jobs.

Yeah go for it JOanna. Gotta cast your net widely; and bear in mind it's what most people are doing already!

Absolutely nothing wrong with applying for several posts simultaneously. It's what you have to do. The only caution is that the more you do, the less polished (and specific) each application tends to be - so it may be in your interest to not do too many.
I was in an awkward situation where it looked like the interview for one job would come before the interview for the job I preferred. Personally I wouldn't accept the first job then go to the second interview in the hope of getting my preferred job, but I know lots of people would.

I just wanted to say that I came the first to this forum because I felt really bad for having two PhD offers. It was a horrible experience.

I also decided not to do the same for my postdoc, but we will see :)

Apply for as many things as you are qualified for - you need to live. If you get several offers and have to reject some that will quickly be taken up by someone else - Win / Win.

Thank you very much for the replies. Uranio after collecting many rejections I realised if I don´t do multiple applications at once I will most likely end up unemployed very soon. Postdoc positions that are a good fit and have funding attached come up very rare.
So I guess applying to as many as possible is the only way to go.
But what happens with fellowship applications? Is it ok to submit a research proposal for funding with one supervisor and at the same time apply for positions with fundng attached elsewhere? Would you inform the first person you are doing so?