Standard American Yellow Card was created by the ACBL many years ago. Its purpose was to conduct sanctioned games in which all players were required to use the same system. While now outdated, SAYC has continued to survive in some fashion. It's sometimes used as a baseline, natural 5-card major system upon which partnerships add their own modifications.
Bidding Notes (86 pages, PDF) by Paul F. Dubois
A thoughtful breakdown of Standard American and 2/1 as these systems are generally played today. It also offers introductory material for newer players, including hand evaluation and educational resources.
Short Club Variant (59 pages, PDF) by Mark Abraham and Griff Ware
A natural 5-card major bidding system with a 15-17 1NT. Its name derives from the 1 opening, which can show an 11-14 balanced and only two clubs.
A Standard American System (60 pages, PDF) by the Eastern Contract Bridge Centre
From a club in Melbourne, Australia. This system uses generic 5-card majors, a 15-17 1NT, and a strong 2 opening. There are a couple wrinkles, including the choice to play either Benjaman or Multi Two-Bids.
2/1 System Notes (383 pages, PDF) by Eric Kokish and Beverly Kraft
A 2/1 game-forcing system by two longtime Canadian experts and teachacoers. Presented as a modified Kaplan-Sheinwold system, it features 5-card majors and frisky 11-14 1NT. A 2/1 response by an unpassed hand is always game-forcing.
Pavlicek System by Richard Pavlicek
An "almost-always" 2/1 game-forcing system with 5-card majors and a 15-17 1NT by American expert Richard Pavlicek. A 2/1 response is game-forcing unless responder rebids his suit. Also of interest is the wide-ranging 6-14 1NT forcing response to 1/.
The Two-Over-One Game Force System (627 pages, PDF) by Neil H. Timm
This 6th edition is a massive treatise on 2/1. It describes the intrinsic 2/1 methods as well as optional gadgets. Neil also touches on topics like declarer play, defensive carding, and competitive bidding against Precision opponents.
Bridge World Standard by The Bridge World
A natural 2/1 system devised over the years by The Bridge World. It employs 5-card majors, 15-17 1NT, and a strong 2 opening. BWS is also the de facto system for The Bridge World's "Master Solver Club" bidding contests.
Kaplan-Sheinwold Updated by Edgar Kaplan
The Bridge World states that these were the last notes written by the late American expert Edgar Kaplan. Kaplan-Sheinwold was a popular system invented in the 1960s by Kaplan and fellow writer-expert Alfred Sheinwold. It features natural 5-card major openings, a weak 12-14 1NT, and weak two-bids.
KS+ — A Modification of KS (113 pages, PDF) by Moty Katzman
Moty has modernized the original Kaplan-Sheinwold system with a Multi 2 opening, RKC 0134, detailed 2/1 sequences, and much more. The opening 2 and 2 bids have also changed to 8-8.5 playing tricks.
Modern Acol (30 pages, PDF) by the EBU
A modernized Acol system with 4-card majors, a 12-14 1NT, and a strong 2 opening. The remaining 2-level suit bids may be played either as weak OR strong.
Imprecise Precision (26 pages, PDF) by Paul F. DuBois
This is a summary of the author's Precision system. It skews toward lighter (and more frequent) bids, including a 12-14 1NT, weak two-bids, and an Unusual 2NT opening.
Blue Team Club (106 pages, PDF) by Arturo Franco and Marco Pancotti; translated from Italian by Daniel J. Neill
A modernized approach to the strong club system played by the famed Italian Blue Team in the 1960s and 1970s. Cornerstones include a 17+ 1 opening, 4-card majors, and a 15-17 1NT.
Polish Standard (106 pages, PDF) by Krzysztof Jassem; translated from Polish by Daniel J. Neill
"Wspólny Język 2005" aka "WJ05" is the second version of the author's Polish Club system. It features a variable 1 opening showing 3 hand types (12-14 balanced, 15+ with clubs, or any 18+). Other aspects include a 15-17 1NT, Precision 2,Multi 2, and Polish 2/ bids showing two-suiters.
Symmetric by Andrei Sharko
A relay system in which 1 is 16+, 1/ are 5-card majors, and 1NT is 12-15 balanced. The response structure is highly artifical, encouraging opener to describe his hand through a series of relays.
SCREAM by Mark Abraham
"Strong Club Relay Excessively Accentuating Majors." A strongish club system whereby 1 shows 14+ HCP. The remaining opening bids are light and aggressive, starting with 9+ HCP. As its name replies, the system makes a robust use of relays.
Relay Club (60 pages, PDF) by Erik Sjöstrand and
A 15+ 1 opening combined with an 11-14 1NT. Other 1-level openings are an airy 10-14 points. Detailed relay sequences after any 1-level opening.
Forcing Pass System (21 pages, PDF) by Don Allen and Trevor Fuller
A relay system in which an opening Pass shows 13+ points. All other opening bids are highly aggressive, showing 12 or fewer points. This includes a 9-12 1NT and a 1 "fert" bid with 0-8 points, any shape.
SPREAD by Mark Abraham
"Strong Pass Relay Ever Avoiding Defending." An opening pass shows 15+ points. The "fert" bid is 1 which indicates 0-8 points. And 1NT is 11-14 balanced.
EHAA+ (13 pages, PDF) by Jari Böling
Based on the original, natural system "Every Hand an Adventure." The primary difference is that 1 shows either a natural bid with 4+ clubs, or a completely artificial 19+ points. All other 1-level suit bids are natural with 4+ cards, and all 2-level suit bids are natural with 5+ cards. For good measure, 1NT is a balanced 10-13 HCP. See also Eric Landau's EHAA FAQ. Good times.
Recursive Diamond (36 pages, PDF) by Adam Meyerson and Sam Ieong
A 5-card major system using 1 as a strong, artificial 16+ HCP. 1NT is 10-12 not vulnerable in first or second seat, or 12-14 otherwise.
Nightmare (52 pages, PDF) by Andrea Buratti and Massimo Lanzarotti; translated from Italian by Daniel J. Neill
A fairly artificial system devised by the authors for the Italian junior bridge team. The 1,1, and 1 openings all have multiple meanings. These are complemented by an 11-14 1NT. It should be noted that Buratti and Massimo were found guilty of cheating at the 2005 European Transnational Teams Championship. They were subsequently banned from the ACBL.