If your appliance requires a voltage greater or lesser than you have in your household electrical system, then you must supply the required voltage. Electronic devices should have a label or embossing with their input voltage, and many like phone or laptop chargers might accept a range of 100 to 250 volts, meaning they can be safely used in both the US and the UK, for example.
I personally moved from the UK to Mexico and have rewired an extension lead so it has a North American plug and British socket outlets, so I didn't have to wire new plugs onto my Blu-Ray player and Apple TV. I don't have to worry about voltage since the supply in Mexico is within the range accepted by those devices.
If you buy a bedside lamp, you'll need to change the bulb, but the rest of the object is just some cable, a switch, and a structure. As long as you're not putting an extremely high power bulb in it that would exceed the rating of its internal cables, you've nothing to worry about, and I would simply go to Home Depot and buy a plug to wire onto it. If you're not up to that, buy a simple but robust travel adapter. This will serve for long term use.
Now you mentioned a coffee maker, my Bialetti was brought over from Italy and I rewired it with a UK plug, but according to the appliance label it requires 220V+ so for use in Mexico I need a transformer to step the voltage up from 110V to 220V (approx., this is Mexico). You have to take into account the wattage (power rating) of the device so you get a suitable transformer.
Frequency (50Hz in the UK, 60Hz in North America) can be a consideration for some devices, as manassehkatz pointed out in a comment, and this would require additional equipment the cost of which would be prohibitive for household appliances.
My recommendation is that a 110V to 220V transformer of sufficient power rating, costing perhaps $100 or less, would be suitable for long-term use with a European appliance that requires 220V, while any device accepting 110V should be preferably be rewired to use a US plug, or, failing that, be connected to an individual non-transformer travel adapter that makes a good fit with both the device plug and the US outlet, or like I do via a foreign power strip wired to a US plug. It is even possible to purchase pre-made strips in this configuration.