Question: Can I use a nonbasic land that taps and gives me either a red or white mana if I only have red mana in my deck?

Answer: 
Yes, as long as you're not playing Commander
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In normal decks, you can use whatever (format legal) cards you want in any combination. You can play a Plains in an all Red deck if you really want to, though it's probably a bad idea.

If you're playing [Commander](http://mtgsalvation.gamepedia.com/Commander_%28format%29), there is an additional rule that says that cards must match the color identity of the commander. This means that your cards can't have any mana symbols anywhere on them that don't match one of your commander's colors. In this case, if your commander isn't at least partially white, then you can't use a land that could tap for white mana.
Quoting from the [basic rulebook](https://media.wizards.com/images/magic/resources/rules/EN_MTGM14_PrintedRulebook_LR.pdf), page 15 ("Building Your Own Deck"):

> 
> You build [your deck] using whichever **Magic** cards you want. There are two rules: your deck must have at least 60 cards, and your deck can't have more than four copies of any single card (except for basic lands).
> 
> 
> 

This only applies to "Constructed" games - the "Limited" format follows slightly different rules; also certain tournament formats may restrict cards to only come from certain sets, and may also ban or restrict specific cards, as per [the banned/restricted list](https://web.archive.org/web/20151004123057/http://archive.wizards.com:80/Magic/Magazine/Article.aspx?x=judge/resources/banned). However, outside of the Commander format there are no rules preventing you from including multi-colour lands unless they are specifically in one of those lists.

If you do include one of those lands, there are a few things to note:

1. It does exactly what it says on it - so if it says "T: Add W or R to your mana pool", then you may tap it to add *either* one white mana *or* one red mana to your mana pool. If your deck has no use for white mana, then you probably won't ever choose to do so, but there's nothing stopping you from doing so.
2. The land is not a basic land of any type (unless some card specifies otherwise). So even if it produces W/R mana, it is *not* a Plains *or* a Mountain (or an Island, Swamp or Forest).
3. As stated above, since it is not a basic land you can not have more than four copies in your deck, or more than one copy if it is on the restricted list for the format you are playing.