To start things off, here are the systems that I play (or used to play), and my general thoughts about them. Later on I'll go into a lot more detail about the reasons for my preferences. But for now I'll just list the systems and tell you which are my favourites and which are, well ...
Acol (weak NT)
This is the system I grew up playing, and so I'm fairly comfortable playing it with any random English partner. As an undergraduate I played Acol for four years with my regular partner David Hodge. It is a perfectly respectable system.
Still, as a bidding theorist I don't like Acol: it seems to me to be terribly badly designed. I intend to use this blog to explain why Acol is bad as much as I possibly can! But that will have to wait for the moment.
Note that old-fashioned Acol contained a number of silly ideas such as Strong Twos which have been almost universally discarded by modern expert players. When I say I don't like Acol I'm not talking about those old-fashioned methods. It's the fundamental combination of weak NT and 4-card majors which causes all the problems. (Some people play Acol with a strong NT, which is not so bad, but I'll treat this as a different system.)
SAYC and 2/1
These are the most popular systems in America and so you come across them a lot online. I suppose SAYC is the "basic standard" whereas 2/1 is "expert standard". But of the two, I actually prefer SAYC, since I've always felt that 2/1 is too inflexible.
This is what I play with Mark Reeve in junior events. In fact we play a very complicated version including "symmetric relay". The complexity of it hasn't really been a problem for us - we both seem to have a good memory for that sort of thing. Though I've never been completely satisfied with the relays: I'm sure it must be possible to do better.
Playing Precision has been very interesting, but I've grown to dislike the basic structure of the system. Still, it's fun to play and I'm not going to ask Mark to change any time soon.
Strong + 4
This is always fun to play. I probably wouldn't play it in a really serious partnership since it pretty much forces you to adopt an aggressive style of bidding, which doesn't naturally suit me. But I believe it's an improvement on Acol if played sensibly. I play strong + 4 with Dan Mcintosh and the Manchester crowd.
Polish Club (WJ or similar)
Now this is more like it. I intend to spend a lot of time explaining why PC is so good. Dan Neill has translated the notes for WJ05 into English and if you're interested in bidding systems this is a must-read.
This is Mike Bell's pet system, though I've had some input as well. It features a "short" 1C opening (used on all balanced hands outside the 1NT range) and a 1D opening which promises an unbalanced hand with 4+ diamonds. This was originally based on the system played by Welland and Fallenius, but a lot of details have been added. I play it with Mike and we think it's rather good.
This is a multi-way club system played with a weak NT, as opposed to Polish which uses a strong NT. The 1C opening then promises 15+ HCP (or equivalent), though it's not really like a normal strong club. The name "Millennium Club" comes from the system book by Lyle Poe. His system includes transfer responses to 1C. I'm not so sure that those responses are a good idea and prefer to play without them. But the real beauty of the system is in the opening bids. I feel that MC is the best way of playing a weak NT.