Common house spiders include:

• Cobweb spider, which requires high humidity and plentiful prey; it typically occurs in damp basements, cellars, crawl spaces, and outbuildings. 
• Cellar spider, found in the dark corner of damp places such as cellars, basements, crawlspaces, and outbuildings.  Cellar spiders can quickly establish large populations in a structure. They are often confused with the “daddy long legs.”
• Funnel web spider, which constructs large, flat, horizontal webs containing a funnel at one end where the spider hides in wait of a victim.
• Wolf spider, which is a hunting spider that’s a fast runner and will chase prey.  They usually occur outdoors, but may wander indoors in search of prey. They tend to stay at or near floor level and construct web retreats in sheltered sites.
• Jumping spiders, which make quick, sudden jumps to capture prey or avoid a threat. They also can walk backward.  Active during the day with a preference for sunshine, their hunting activities often center about windows and entry doors where their prey is most common.

(From Ohio State University)

• Yellow sac spiders,  invade structures in the fall when the weather turns cool and their outdoor food supply disappears.  Indoors, they can be observed on walls and ceilings, but drop to the floor to seek cover when disturbed. Their small, white, paper-like sacs are often found in easily overlooked locations, along ceilings and corners, or behind pictures and shelves.  Experts believe sac spiders cause more bites than any other type of spider.

(From University of Nebraska)

Daddy-long-legs, also known as harvestmen, are commonly mistaken for a spider due to their general appearance and eight legs. Daddy-long-legs are usually not encountered in living areas of a building, but are more often found in crawl spaces, basements, and outbuildings.