You can open only one cash ISA in each tax year.
The following tax year, your allowance renews so you can open another ISA, with another provider if you wish; so the answer to your question is yes you can take out more than one ISA; providing they are not in the same tax year.
Gizmonster is nearly right. You can only pay into one ISA each year. You can open several but only by transferring money from another ISA. I opened 2 last year.
Cash ISAs and Shares ISAs are classed as different, so you can pay into 1 cash ISA and 1 Shares ISA in a given tax year.
Yea .... just to clarify, when using your new tax allowance, you can only pay this into one cash ISA per year. If you've got any existing ISA's, you can transfer to other existing ISA's or transfer them into a new ISA.
You can split your allowance between a cash ISA and a stocks and shares ISA as well. This year's allowance is £20 000.
It's always worth going to the Martin Lewis site too for info like this.
I agree with some that ISA rates are not very good, often easily beaten by non-ISA rates - and with the tax free savings allowance in place ISAs are only of any use to those with large historic ISA balances as a safe haven for a future date if /when ISA rates improve