Legal ways of playing old games that aren't for sale any longer
Solution 1:
Basically, if it's not on something like WiiWare, Playstation Network, or Good Old Games, or re-released ala many of the Nintendo era Final Fantasy games, then you're going to have trouble finding copies and the equipment needed to play them. The fact that certain games are simply nearly impossible to purchase anymore is often the excuse for abandonware or ROM sites. It is worth pointing out that if you buy a copy on ebay for $100, the company that owns the game won't actually see any of that money. Whether this goes against your moral compass is up to you.
That said, legally, it'd be against the law if you download a game, even if it's not being sold anywhere. Fortunately, more companies are joining the bandwagon of releasing older games for new audiences, so it's become easier to find old games for sale legally.
Solution 2:
Using ROM images from the net, or even from a copy of a game you own, is illegal. Period.
Here is Nintendo's official take on it
If you want to be legal, you have to buy the original system or a licensed re-issue and the original ROM.
As these games are out of circulation, and as such are practically relics by modern media standards, you've got to choose your battles.
Finding Them Cheap/Free:
If you want to be thrifty and save a buck, you're going to have to hunt around and do the leg work. These items can be found at many vintage/thrift/flea market locations... often for 99¢ So you could scour the wastelands and possibly score one. It won't be MIMB... But it'll play your games.
If you REALLY love the game just buy it. No price can be put on love! Own it and treasure it. Archive it. Take pictures of it with you on vacation and frame them.
And check Craigslist. People often GIVE AWAY old stuff like this.
You are essentially collecting art and design from the past... just with the added bonus of light, sound and interactivity. Sometimes really amazing pieces of the historical past of video games fetch VERY high prices. If that is the case, just owning it can be a fight. Be prepared.
Places to Buy Old Games:
There are a lot of places that ship and have online inventory or are only a phone call away.
I can personally recommend eStarland - They have long been a leader in online retro and import game support.
8 bit and up / 212-674-0201 - Very cool owner, and great shop.
Video Games NY / (212) 539-1039 - Has a huge selection
You can also purchase a reissued console that plays both NES and SNES (and Sega's SMS/Genesis - score!) cartridges for about $30
CNES/SNES/Genesis FC3 Plus Gaming System
These systems support the original cartridges. And are also legal.
tl:dr
In short, collecting vintage via the internet isn't always cheap. To save money you're can try questing around the country side of suburbia. MILLIONS of SNES systems are always around. Plus it's always good to get out of the house, off the net and meet your neighbors!
But, unless you own a time machine, be prepared to be the high bidder or forever be incomplete in your collection if you're after a hot or controversial title.
Good luck!
Solution 3:
A lot of the other answers are long-winded and in-depth, so I'll take the short route.
You basically have three options:
Buy a copy of the game. Used game store, yard sale, eBay, pick your poison. This only works if the game is still available or still working; some games with battery-powered save-RAM (or worse, battery-powered program-RAM, like some arcade boards) will cease functioning, so this won't be an option. The older the game or the less copies that were made, the more expensive it can be, up to several thousand dollars if you want to "legitimately" play a very rare game. Note that the original vendors get none of the money from this option.
Get it off your favorite official download source. Virtual Console, PSN, X-Box Live. This only works if the game has actually been released on the service, which requires that the owning company still exists, still has the proper licenses, and such things. This is why you'll never see Earthbound on there -- lawyers afraid of licensing issues due to the music and references. Note that even if a game does see release, they're usually modified from the originals. Tecmo Bowl, for example, has all of the team names and players removed.
There is no three. If you've got to this step and still don't have your game, sorry. There's really nothing more you can do. Your only option is to find a copy of it online, download it, and pledge to support your favorite developers should they ever release the game again, or perhaps purchase related merchandise. Writing a letter to the developers inquiring about a re-release optional, but may make you feel better.
Sorry to disappoint, but in many cases you will end up going to option three.