So, if you use synthetic, you still change the filter at the recommended interval?
It depends; There are extended interval filters that are good to 15k or some good to 25k miles. Even a "regular" filter though should be good for at least 5k miles, maybe even 10k miles.
Some things I want to say to maybe clarify the synthetic/conventional oil debate:
Just because oil is synthetic, you can't say it's good for X miles. There are different types and qualities of synthetic oil. Some lasts 5,000 miles, some 7,500 miles, some 10,000 miles, some 15,000 miles, some 25,000 miles, etc... The use matters as well; if you race regularly, tow regularly, etc... the oil probably won't last as long.
I like synthetic oil but still like to change it often because I prefer to flush/cycle it. I change mine at about 7,500 miles and use Amsoil OE oil(cheapest amsoil oil) and use a WIX filter. I sometimes race/drive hard so I don't want to push it. The oil is usually black by the time I change it.
Conventional oil is typically good for at least 3,000 miles. Now the maintenance schedule in my truck says I think 6,000 miles or something, and you can use conventional. I'm sure it would be fine, but it is probably pretty well broken down I'd bet by that time. The synthetic should hold up much better at that mileage(even cheap synthetic).
There are bad filters (cheap frams for example) and good filters (WIX, Napa, mopar, etc...) and this has to due with the type of seals in them (cardboard vs rubber) and the type of drain back valve (if it even has one). There are also "regular" interval filters and "extended" interval filters. If you change your oil anything under 10,000 miles a regular filter should suffice. If you go beyond that you probably will want a extended interval filter or change the filter in between oil changes.
Basically just because an oil says it's good for X miles doesn't necessarily mean that's spot on, it depends on MANY variables, so the best thing to do is pick an oil that fits your needs (mileage based, time based, and use based) and monitor it to see how the color of it changes, and more importantly how the viscosity of it changes. When it gets black and more importantly "watery" instead of "oily" then it's time to change it.
I hope this helps at all...