Q:

Bring Your Own Mic

Should I bring my own mic to open mic nights?   I like the sound I get from my mic at home, and I spent alot of money on it.   I have found that mics at various open mic nights are inferior to mine.   So the sound isn't what I am used to when practicing at home.   

A:

In my opinion, definitely not. 

As a performer, there will always be aspects of a venue and the set-up that are unfamiliar or at least not ideal.   Learning to adapt is an important skill. 
Your mic might not work with their setup. 
Swapping mics, adjusting volume and EQ, etc.  is going to take some time.   Will they accomodate you?   I'd say it's just going to reflect poorly on you.   It may not normally be very much work to set up a mic but you're still inconveniencing them for a minor benefit. 

A:

I think the answer can vary depending on the situation.  I think judgement is imperative.  If you're doing one 5 minute tune, and the mic change takes you two or three minutes… it's probably not an appropriate request.  If you're performing for twenty minutes and it takes you two minutes to setup… perhaps not.  I'd say from what you're describing, and at the open mic's I've seen… they might look at you a little weird, and it probably wouldn't be appropriate to even ask.  It would make you look silly if you insist on changing their setup for a tune or two, just because you're used to it. 
I also agree heartily with @Matthew Read's comment about learning to adapt.  If you think adjusting to someone else's microphone is bad, think of a piano player who has to adjust to a whole different instrument every time they play.  Grand pianos, even good ones, vary significantly in tone and playability.  
It's something to consider; the better you can make yourself sound on varying setups, the better musician you'll become. 
Hygiene could be a concern, but just project your voice so you don't have to swallow the mic.  If you have a legitimate hygiene concern, like a compromised immune system, or a communicable disease yourself, this could change my recommendation, but definitely be open about that with the venue.  

A:

Swapping the mic isn't going to make you sound like you do at home, I'm sorry to say.  There's a certain sound you tend to get at open mics: Boomy, too much reverb, and designed to cut through an indifferent crowd.  Monitors may or may not exist, it's more likely you'll be hearing yourself through the mains behind you.  A PA setup and EQd like this almost certainly can't take full advantage of the mic you bring.  
I think it's same to assume that the open mic won't have a dedicated engineer. ( At most, they may have someone working the board in between filling drink orders.)  While I know of some open mics with a sound guy and a nice PA (like the one at Artichoke Music in Portland, OR), these are rare.  Having an engineer makes swapping a mic the work of ten seconds.  It'll take a few minutes without one, which will cut into your set time - or worse, you'll go long and piss off the performer after you as well as the crowd.  Crowds hate it when an act at an open mic goes long.  
By way of perspective: 
As a part-time engineer at festivals, I've had incredibly picky singers on my stage, who can't sing unless they hear the piano or the guitar too loud, or (most commonly) they need to hear their own voice a lot.  Or awash in echo.  Or with a chorus pedal.  
In a small room, where the monitor mix spills into the front several rows, these performers can present a challenge.  
On the other hand: I've encountered singers who can sing into anything.  These people are amazing, and have obviously played many venues.  No monitors?  The band won't turn down their backend amps?  No problem!  I trust you, sound guy, I'll sing my heart out and you'll make me sound great!  You want to be one of these performers if you can.  
So, back to open mics: Playing at many different venues, with varied setups, will teach you flexibility.  You'll learn to adapt to great PAs, bad PAs, no PA, bars where the TV is louder than the PA. 