Yes, they will load. AND they will typically load the iPad native version of the app if it is available.
That actually depends on the developer.
There are three things that can happen:
1) The developer has only released an iPhone version of the app. If this is the case, you can run them in a tiny spot in the middle of the screen, or as a "2x" version like Lance describes.
2) The developer has included both iPhone and iPad views in the same app - These apps are the ones that have a little "+" in the corner of the price buttons on the store. In this case, you'll have a nice iPad-native version of the app without having to do anything additional.
3) The developer has written separate iPhone and iPad apps. Some developers, rather than adding iPad views to their iPhone apps, split them into two separate apps so they could charge you more money by making you pay them again to get the iPad app. Bad form, IMO, and luckily it's not too common. If this is the case, you'll basically get the iPhone-only version on the iPad just as in case 1) above, but if you want the nice iPad-native version you'll have to pay again. (Be sure you let the developer know how you feel.)
I actually don't have a whole lot of apps that I use on both devices - I discovered fairly quickly that most apps really shine on one device or the other. For an app like ForeFlight, it is so much nicer on the iPad with all that screen real estate that I rarely use it on the iPhone any more. OTOH, I don't like TweetDeck's implementation on the iPad and I often use it in situations where I don't have the iPad with me (though I do still have it on both devices). There are actually quite a few apps whose functionality is fairly simple that work great on a one-handed small-screen device like the iPhone but wouldn't be as useful on the relatively bigger and clunkier iPad.