Pinball Hall of Fame - The Williams Collection features machines from as far back as 1970 all the way to 1990. You will get to relive the experiences of Gorgar, Firepower, Black Knight, Sorcerer (one that caused me many headaches), Taxi and Whirlwind (plus the machines mentioned in the previous section).
As far as I know, there have only been a couple of Pinball Hall of Fame games, the last one that I am aware of being The Gottlieb Collection, which, if memory serves, Psibabe didn't find all too enjoyable, or at least there were enough problems with the game to cringe at the thought of another one. Thankfully, it seems like most of the issues have been worked out for The Williams Collection because I never felt cheated while playing the games and seemed to be satisfied with the physics of each machine.
There are a few gameplay modes here. The most straightforward is Practice Mode, where you take your credits around the arcade and play the various machines. You earn Credits by playing in the other modes, but there are also a few ways to unlock a table's Free Play Mode. The main way to achieve this in Practice Mode is to play a table so well that you achieve all of the goals the game has set aside for it, or you can just save up enough credits to buy the table outright.
The Williams Challenge Mode takes you through a set series of tables allowing you to advance to the next one only when you have surpassed a goal amount. Once you have beaten a table, it becomes available to you for free in Practice Mode. The odd thing about this mode, which makes sense from a replay perspective, is that you can't just leave the challenge and go back to it where you left off. Just because you beat the Black Knight challenge, doesn't mean you can skip the entire table before it in order to advance.
The last mode is Tournament. Here, up to four players can complete (even on tables that didn't originally support multiplayer) and standard Pinball Tournament rules apply as far as point tallying and winner determination.