Sorry if this is redundant (the post said there was 1 reply but I don’t see it here).
Anyway, the answer is “kind of”. Exporting as OBJ, FBX, Alembic and .3ds can all have their textures transport with the geometry (adn in some cases animation too). In some cases you will get one big model as on piece when you reimport it but depending on the importing package you can often break that model into it’s original groups that it had in C4D. Now, whether the textures stay intact, stick to the faces you had intended or keep the same scale is another story – some packages even swap Z for Y.
Often when exporting you get to choose what units you are working in (m, cm ,mm etc) and which way is “up”, so check the export settings in the C4D preferences for the file format you are considering. Make sure who ever re imports it brings it back in at the same units. When exporting you don’t always get a “choose your settings” dialogue but there is one in the prefs for each format.
Keep in mind that things like procedurals (primitives, deformers etc) may not translate and should be made editable or “current state to object” to collapse them into pure polys. This goes double for matrix type objects (mograph etc)
.3ds is probably going to be the most lucky – its such an old format that things have to be made so simple, its hard to screw it up. FBX is probably the next best (and can include the animation). And Alembic the next (this one should be the most robust but not every package is supporting the full format yet). OBJ is the most simple so is usually the easiest to fix when it goes wrong but it’s a gamble – no animation here.
Things like Hair and particles won’t translate at all.
Finally, the render engine will be different so your carefully set up lighting might look very very different.