I was already someone inclined toward saving and being a cheapskate, so maybe take this with a grain of salt. That said, MMM helped me establish a framework and a financial goal, where previously I was just hurling however much money seemed available into a savings account and then doing nothing with it.
1) Tracking every penny of my spending. It had the dual effects of forcing me to be accountable for all my expenditures-- every purchase, no matter how impulsive or frivolous, got logged, and demystified my own spending habits, good and bad. Doing this also answered important questions like: 'just how much do I need to live on anyway?' 'how much am i eating out compared to how much i cook at home?' 'just how much money did I save last year?'
2) Making savings automatic. Can't spend it if I can't see it, and can't even miss it, really-- whether it's an automatic push of $X amount into a savings account or upping your 401k contribution, that really helped me focus on staying within budget, and padded my stash without conscious effort.
3) An actual change in mindset (plus side: FREE, downside: HARD) away from the 'buying things equals happiness' cultural mindset that's so damn pervasive, and actually putting thought into how a new purchase will fit into my life-- where will it be stored, how will I use it, how long do I expect to keep it, and does it fill a need in my life that is currently empty? Do I still lust for random things? Hell yeah. Do I still buy them after some thought? Well... sometimes! But the things I buy now actually make me happier, and has resulted in so much less clutter, spending guilt, and a much fuller wallet.