I've ordered from SGP and one or two of the others, without any problems. SGP offers both UPS and Priority Mail for smaller items.
Here's a list of the online / phone order vendors that I know of:
Subaru Parts Mail Order Vendors
* 1stSubaruParts.com WA, Renton Walker's Renton Subaru
* (Annapolis Subaru) MD, Annapolis Annapolis Subaru ('SubaruPartsGirl' on SubaruForester.org)
* FredBeansParts.com PA, Doylestown Fred Beans Subaru [NASIOC vendor]
* ShopSubaruParts.com AZ Chandler Subaru Superstore of Chandler
* SubaruGenuineParts.com WA, Bellevue Chaplin's Subaru
* SubaruOnlineParts.com NY, Hicksville Grand Prix Subaru ?
* SubaruParts.com WA, Tacoma Tacoma Subaru
* SubaruPartsCenter.com ? ? (also SubaruPartsPro.com)
* SubaruPartsForYou.com CT, Milford Dan Perkins Subaru
* SubaruPartsOutlet.com WI, Milwaukee Schlossmann's Subaru City
* SubaruPartsPeople.com "Pacific NW" site: Carter Subaru Ballard Seattle, WA
You should check parts availability, shipping rates/times, return policies/restocking fees before ordering.
Be aware that all of them (just like your local dealerships) don't stock most items -- they'll need to order from their regional Subaru warehouse. Sometimes, parts will have to come from Japan.