generally controlled induction with a molecules as iptg is necessary when you are expressing protein that is toxic for the cell because otherwise you can observe poor bacterial growth if protein is expressed to early, while using the iptg you can induce the protein expression during tge exponential phase and limiting the affect of the toxicity.
However in the last 10 years autoinduction become more popular expecially for high trhougput approaches because it is certanilly more simple.
the presence of basal expression depends from the e.coli strain, expression vectors and expression media that you use.
As Fadii suggest in some cases you can have basal expression prior induction. This for example happen more frequently using promoter as lac or tac that respect the t7 are less repressed but also in t7 promoter you can minimize basal expression by choosing a media which contain glucose or a strain as plyss or lemo de3 genetically modified for this purpose or on the contrari you can push up basal expression on standard bl21(de3) strains using media with out glucose and rich of yeast extract.
You can find some examples on my blog : https://proteocool.blogspot.com/?m=1
ProteoCool n°5 (E.coli high cell density media overview ) at page 2.
where i report the properties of Enpresso which is a strong repressed media which require IPTG and YGR which is a poor repressed media suitable for autoinduction.
The importance or IPTG is entirely dependent on what promotor system you are using to express: If you use the T7 promotor and lac operator together with the lac repressor, you have a system in which expression is very low in the absence of lactose or its analog Isopropyl-β-D-thiogalactopyranoside (IPTG), and can be further supressed by addition of glucose. This is used when expressing genes toxic to your cells. you keep production of your protein tightly suppressed to keep your cells healthy and growing until the cell density is high enough to start production.
In cells that do not express the lac repressor, you get expression even in the absence of IPTG.