Disclaimer:
I am not a lawyer.
Copyright laws differ per jurisdiction.
What I've stated below is the norm in most countries.
Downloading a ROM is illegal.
No matter whether you own it, or whether you only keep it for a few hours, it is always piracy.
See the Nintendo FAQ on the matter for more information.
In case you don't trust Nintendo because they are partial to the subject, the WIPO Copyright Treaty explicitly prohibits circumvention of technological measures and unauthorised modification of rights management information in articles 11 and 12 .
As for your second question, there are a few options you could try.
Like Martin suggested, you could try going into a game shop and see if they have a console you can try it on.
There are also options to rent a game instead of buying it, and you can always buy it again afterwards.
Alternatively, if you are committed to circumventing copy protection in order to play illegal copies of video games, might I suggest moving to Monaco.
On balance, it is a far more desirable place to end up than say, Nigeria.
gaming.stackexchange.com/users/None/
I'm fairly sure from my view on this, that it would be illegal in most countries, as you are not the legal owner of the content to begin with.
It does sound morally right to delete it and then buy it if you like it, but at the same time it's not legal.
There are some solutions for it though:
Rent it.
There are still video stores out there that will rent a game for perhaps $5 a week or so.
Play
N' Trade .
This store is only in the US, but they have tons of TVs and consoles set up so you can TRY before you buy.
I think it's awesome.
Ask around with friends!
Social networking may help with this, just drop a post on Facebook/Google+/Twitter/Whatever you use.
gaming.stackexchange.com/users/9448/Simon Sheehan
Check your local public library.
More and more libraries these days are offering games for checkout.
And it's probably free as long as you return it on time.
Some libraries may require a deposit to borrow games/systems.
gaming.stackexchange.com/users/1804/aslum
Gamefly?
Rent from a brick store, if you can find one still standing.
gaming.stackexchange.com/users/11615/normanthesquid
I can only speak for the greater Indianapolis area, but I would be surprised if this doesn't hold true elsewhere: Official policy or not, GameStop employees will accept returns on the grounds that you don't like the used game that you purchased.
If you are seriously considering buying a game and want to try it first, buy a used copy from GameStop.
This doesn't mean you get to use GameStop as a free rental store; If you like the game, keep it.
If you're talking about games that you can download from the Wii Shop Channel, the only legal way to try before buying is to play the purchased game on a friend's system.
(Nintendo is shooting itself in the foot by not providing demos in the Wii Shop; If you don't know someone who bought the game, you truly have no legal option for try-before-you-buy.)
gaming.stackexchange.com/users/12094/Jake
How about OnLive?
http://www.onlive.com/
Sure they don't have many games at the moment, but they might have the ones you are looking for?
gaming.stackexchange.com/users/12064/RiddareRalf
GameFly.
It's been said before, and I recently just canceled my subscription, but for legal ways of trying games, this is probably still one of the best options.
They have a good selection, allow you to hold onto the game as long as you want, and generally have decent service in terms of re-shipping lost games, etc.
Their used prices are actually pretty good, so if you're interested in buying a game after trying it, you can get them to ship the box and manual for a game just by paying the used price.
(even if you're the first to rent it) I've done that quite a few times
and it's a great way to buy a game AND get them to ship your next game ASAP.
I don't think you were hoping to hear "a paid subscription service" as an answer, but it really is among the better options available, even if not ideal.
gaming.stackexchange.com/users/10246/Tux
To add on to the other suggestions, I also agree that your current method is illegal.
Game Stop allows you to return used games (I don't know about new) before a certain number of days pass (I don't know how many)
gaming.stackexchange.com/users/3638/Scott Chamberlain
I assume by your question you are referring to the downloadable games for the Wii, not the retail titles.
Some games, like Super Smash Bros. Brawl have unlockable demos for classic NES games.
For any disc-based title, just rent it from any game rental store/service.
gaming.stackexchange.com/users/9300/CyberSkull
The only method I can think of is to download a ROM and test it with an emulator, and then delete it 72 hours after I download it. However, I'm uncertain if this is legal.  How can I test a Wii game before buying it?
How can I legally try Wii games before buying them?
gaming.stackexchange.com
<nintendo-wii>
gaming.stackexchange.com/questions/28983
gaming.stackexchange.com/users/12046/Saulius
You can go to a gameshop and see if they have a console you can try it on. You can also rent games before buying them or buy a used copy. Renting it, testing it in stores or asking friends are the most prominent solutions since downloading is illegal.
Τhere is not any legal option in downloading games. There are several ways to try a game such as rent it, buy and return it, or ask a friend.