What kind of captcha are you using? If it's the image captcha, it is possible that this is being broken because image captchas can be cracked. As far as I know there is a mod available for a trivia captcha.

But if you've got the more recent text one already it could be that it's being broken by people paid small amounts to fill them in, people in the third world, for instance.

Have you disabled your member list so that it's not viewable to guests, and disallowed signatures from members who haven't made many posts?

The trouble is, PhpBB is always going to be targeted for spam registrations because of its popularity. The real answer is to move your board to software that makes it easy to remove footprints such as the "powered by" text and other tell-tale signs. Once you move off the beaten track by customising software your spam problem will be greatly reduced.

Its the standard phpBB captcha (latest version). The registered accounts seem to be all random letters or a name followed by random numbers so it looks like bot activity.

If it is being done by people (or bots) they don't get far as you can't post URL's until ten posts and seven days membership has been achieved. Its just irritating to have all these fake spam accounts and very time consuming to delete them all individually.

Yes, all the usual steps have been taken, memberlist gone, websites and sigs banned, "powered by" removed.

So there is no solution to this one then and we have to live with the spam bot accounts?

The captcha I'm suggesting isn't the standard one, it's a text one rather than an image. Look up Prime Anti-bot or Anti-Bot Question on the phpbb forums. These are optional mods that might help.

A strong captcha in combination with a question simple for humans ("What is two plus five?") should slow down the bots.

Which phpbb version are you running? To the best of my knowledge the phpbb3 GD captcha hasn't been broken yet. For that matter you can turn it up to point that it becomes unreadable as its adjustable. At some point it will become useless but at the present time it should work fine. Note that I said GD, the imagemagick option only produces the phpbb2 style image captcha which is useless.

phpbb3 does take a lot of other measures to deter the spammers, by default the memberlist, profiles and I'm pretty sure signatures are hidden from guests. So that only leaves posting as a way to get a link posted.

If you're still running phpbb2 one of the question mods should stop them dead, did for me. There's a big thread on phpbb.com with a list of all the anti-spam mods and ways to stop them.

Thanks for the replies, I'm on 2.0.23 and have installed a basic "authorization code" mod which has slowed them down a bit.

Try "The Humanizer [phpbb.com]" mod, it does what rogerd suggests. Be diligent and create your own question, don't rely on the stock Q&A the mod comes with, as even the mod creators suggest you change it. It's very easy to implement, took me about fifteen minutes to do.

Good luck.