All great feedback, but I’m wondering if what you’re asking is: if I get a flat while out on a ride in the boonies, will I be able to fix it on a bike with spoke wheels?
Short answer is: probably not. Here’s why.
Spoke wheels: As mentioned, spoke wheels have tubes and loss of air means the tube has blown or has a hole. To fix it, you’ll need to removed the wheel, remove the tire, put in a new tube and then put it all back together. Adventure riders live for this stuff, but most of us are not prepared or wanting to do this kind of thing. Typically, this means a call to AAA or your BFF with a truck.
Cast wheels (no spoke): No spokes usually means no tube, so it’s just like a car tire. If you’re lucky, the flat was caused by a nail or something similar. Pull the nail with pliers and then use a glued tire plug to seal and you can be back on the road in a few minutes. It’s wise to treat the tire gently and I’d probably cruise back home or to the nearest cycle shop to get the tire inspected and either replaced or properly patched on the inside. As megaspaz said, a puncture in the sidewall (too muh flexing) or a slash means you’re toast and puling out the cell phone.
As for spoke tightness, you should occasionally inspect the spokes by pinching then together in pairs (with your fingers) to see if they are uniformly tight. If you find a few that are significantly looser, it may indicated that your rim is going out of true. This is an easy fix at any cycle shop. If you’re out of the road, unless you just hit a curb, I wouldn’t fret about the spokes.