The peace issue is a big one for me.
Working together helps build understanding and break down barriers.
Many parts of the UK have benefited from EU money for building projects (usually the poorer parts) - we never shout about it because we don't like to admit we have areas that are poor enough to benefit. (Many roads and ports in the remote parts of Scotland have been funded by EU money).
UK students can get Erasmus grants to travel and study (not necessarily abroad) - I did an MSc funded in the is way (6 months in Scotland, 6 months in Strasbourg).
Science (and probably arts) collaboration - large amounts of research funding (of which UK gets a big share than we warrant from purely per capita share) comes from EU and involves EU collaboration. I read in the New Scientist that Switzerland is currently suffering very badly because it can't be part of these projects at present. I think our science effort would be decimated if we lost EU funding (I don't see our government throwing much money into it).
Ease of travel, ease of moving to work in other countries, reciprocal medical agreements, ease of trade between countries.
I also think we benefit hugely from the environmental legislation (we don't have a good track record of bringing those things in ourself, although we are better than many in complying once forced on us).
I think the bottom line is - the EU is the cause of all our problems, if we leave it, it won't magically solve all our problems, and will create quite a lot more that most of us are unaware of.