So, there's a lot of lore in the books that covers this.
Burning Bright is the one that most comes to mind as it features a mage, his ally spirit, and about a half dozen spirits he summons. Its been a long while since I read the book, but I do remember some of the interactions between the spirits and the mage.
The Ally Spirit was an "under the breath" comeback sort that always had a sharp retort for every thing...
The watcher spirit was basically a talking dog... loyal, happy to do tasks... and forgetful of said tasks until reminded... (as in, it would complete the task as it had to as a watcher spirit... but would then forget to report back and just wander about observing things until the mage actually recalled the watcher).
The was a fire elemental he used in combat (this book was written in the 2e days). which was mostly a static block of fire personality wise.
Through the editions, Spirits have changed dramatically. Originally from editions 1 to 3 Spirits and Elementals where two separate things, and behaved in different manners.
Mages summoned Elementals (earth, air, fire, water), and they were described at basically being automatons, with little if any personality. Shamans summoned Nature Spirits (land, sea, sky, hearth, man) They were described as having a personality linked to their domain...
Things changed with Universal Magical Theory that was introduced in 4e (and still in play).. That basically threw out everything about magic and spirits and elementals from previous editions and "streamlined it" (I call it "removing flavor in favor of contradictions". To each their own)
Since then, I have sadly not read much fiction involving spirits, aside from what's in the rules books.
Spirits actually like to come to the material plane! This is why they "agree" to the summoning in the first place. (page 300 of the CRB, red box that the bottom: Heading: Spiritual Relationships)
Most spirits seem to like being on Earth, but the exact reasons are unclear and the spirits are not
keen to share any information.
What Spirits don't like is being Bound.... (see Binding, page 300 CRB)
The best way to thing of Spirits is like CanRay said; As people. Anything you would consider abusive as a person, Spirits would too... including committing mass mayhem and murder for a mage, or being ordered to be a "meat shield" for a mage... (Cause I know I get really pissed when people ask me to burn shit down or beat up someone... and I get really pissy if I get bopped in the nose cause of someone else...)
Street Grimoire page 180 as a great fiction about what happens if you mistreat spirits.... and after that work of fiction, you have 20 pages all about Spirits and the official "who, what, where, why, and when" of Spirits.. (and its up to date, thanks to UMT)
The TL/DR?
Yes it is possible for Spirits to be friends with a mage, outside of the Spirit/Summoner relationship, but the reasons for why a spirit may want to call a Mage a "friend" is not clear, and may not even be a "human" response to such a question.
I have allowed in my games for character to pick up FREE spirits as contacts (and improve the relationship to the "friend" stages through roleplay and karma)
BUT, I would be a little hesitant to allow a summoned spirit to be a contact...
But friendly and helpful to a mage? Maybe even offering help without services after a period of exceptional behavior? (and other hallmarks of friendship) Sure, why not?