Unless you're talking about fairly substantial amounts, and have some .... erm .... inventive tax arrangements, I'd advise forgetting about offshore accounts.
Firstly, the existance of an offshore account is a red flag to tax authorities, if they find out about it. And in recent years, especially in the light of post-9/11 money-laundering regulation, the "numbered" account has all but disappeared. It's a myth in relation to Swiss banks, and Caribbean tax havens don't dare cross the US too overtly. Therefore, the "know your customer" requirements of the Patriot Act make it VERY hard for tax haven regimes to operate with the US (or EU) unless they comply with such requirements.
Opening a Swiss account is not difficult, but it'll cost you to open (anything from a few hundred pounds to a couple of thousand, typically), and you'll get transaction charges unless you maintain a fairly healthy balance. If you're talking about investing as few hundred from your monthly pay check, it's most unlikely to be worthwhile, especially given that Swiss banks now charge a flat tax on all accounts from EU citizens.
It is certainly true that there are still advantages in Swiss banks, not least of which is that regulation on disclosure to third parties is very strict indeed. So if you're seeking to hide funds from your spouse, for instance, it's great. One reason it's great is precisely because the Swiss banking industry is so tightly regulated. While this regualtion menas limited scope for illegality, it also means that Swiss banks are FAR more stable and trustworthy than some back-street outfit on a Caribbean island. If you go for the Caymans, etc, be very careful about your choice of bank. But for small balances, or for tax avoidance (even perhaps tax evasion) Swiss accounts are not worth the cost or effort.
Where these types of accounts still come into their own is for proper tax avoidance schemes. For instance, if I incorporate a company in the US, it's worldwide income is going to be subject to US tax provisions. If I then incorporate a company offshore, and merge that US company into the offshore one, I'll still find that US operations are subject to US tax provisions, but worldwide operations aren't. Yet, the US company can still be US-listed, but the parent company is offshore. If you do this right, it can save fortunes in tax, and is perfectly legal and above board. I can do it quite openly.
However, as soon as you start trying to do things secretly, you'll hit problems with funds transfers between national jurisdictions raising security service red flags. You'll also find that Swiss banks cooperate FAR more with national authorities than they used to, and that tax fraud is certainly something that WILL allow the Swiss to open banking secrecy and cooperate.