Some companies pay a one-time commission to you on each sale and have no compensation for a downline structure. These are okay for a little extra pocket change, but don't spend much time on them. If you can just stick a banner on your website and get a couple of sales a month, go for it. That isn't bad for the 10 minutes of work it takes to get the banner there. Just don't blow your whole advertising budget on this type of affiliate program.
Some companies only pay one or two levels deep in a downline.
That is fine if the commission percentages are relatively high. Remember you won't have very many downline members working for you in these structures. Other companies pay you commissions for many levels of your downline. These work fine if you intend to build a large downline, but you will find the commission percentages are much smaller. Downline structures take on many forms.